Advanced. Questions. Whenever we multiply expressions together with the same index this operation is equivalent to adding the numbers in the index together. Worksheet Answers. NPm0!"9:!@Q:A=w+rBfj J23~l"A=x[bn/e#88Y^-UG7^7!j,xH K/[{_r;^^Tb2l `wNA&:@ ":h _ come with answers. Types of Numbers. << /ProcSet [ /PDF /Text /ImageB /ImageC /ImageI ] /ColorSpace << /Cs1 7 0 R Indices show where a number has been multiplied by itself, eg squared or cubed, or to show roots of numbers, eg square root. Name: Level 2 Further Maths Ensure you have: Pencil or pen Guidance 1. You might just want some questions for a bit of practice. E.g. &=\frac{1}{(2b)^{4}}\\ am an = amn a m a n = a m n. Step-by-step guide: Dividing indices. for using this wonderful free resource, and to get hold of the right!? Therefore, 7^2\times 7^ {-6}=7^ {-2+6}=7^ {-4} 72 76 = 72+6 = 74. Corbettmaths Primary Primary 5-a-day, videos, worksheets and more. Download the medium term plan by clicking on the button above. Indices and powers. have kindly allowed me to create 3 editable versions of each Worksheet - Negative and fractional indices. K439:Raise an Algebraic Term to a Positive Integer Power. 5-a-day GCSE 9-1; 5-a-day Primary; 5-a-day Further Maths; 5-a-day GCSE A*-G; 5-a-day Core 1; More. 110. The terms are being multiplied. authorised service providers may use cookies for storing information to help provide you with a You must show all your working out. Log in above for the teachers version. GCSE Maths Specification and Awarding Body Information Videos . So, we get that 4^ {-3}=\frac {1} {64} 43 = 641. 1. On most occasions the positive root is the only one required. K440:Raise an Algebraic Term to a Negative Power. Caluculate a power raised to a power Corbett: Laws of Indices Collins: p50 Use Negative Indices. Negative Indices Textbook Answers - Corbettmaths. This worksheet features converting negative indices into fractions and vice-versa as well as converting decimals into index notation. better, faster and safer experience and for marketing purposes. A Level Revision. (c) Deal with problems involving a mixture of bases. Write the following as fractions without indices: a. KS1 KS2 (Lower) KS2 (Upper) KS3 GCSE Foundation GCSE Higher. Level 2 - Evaluating positive indices with a calculator. Using all 3 laws of indices . A farm has an area of 12 km 2. 4 is the base and 3 is the index. It really is one of the very best websites around. 2 0 obj negative_indices_answer_sheet.pdf. James Corbett Because even if u are a shark in maths u one day u will find difficulty in something, just take a picture, crop out the problem, and bam. Step 3: Simplify to get the simplest form of the fractional index. They Indices Name: _____ Instructions Use black ink or ball-point pen. corbett maths negative indicescuanto cuesta quitar una caries en colombia. The last two questions apply the same ideas to algebraic expressions. Where pupils have these pre-requisite skills, we recommend adapting the questions (where appropriate) to include this content. Step 1: Simplify $$\left(3x^2y^2\right)^2$$, $$\left(3x^2y^2\right)^2=3\times3\times x^4y^4$$, $$\left(4xy\right)^3=4\times4\times4\times x^3y^3$$, Step 3: Use the rules of indices to simplify them further, $$\frac{\left(3x^2y^2\right)^2\times\left(4xy\right)^3}{24x^4y^7}$$, $$\frac{3\times3\times{x^4y^4}\times{4\times4\times4\times}x^3y^3}{24x^4y^7}$$. September 2, 2019 corbettmaths. Powers, Roots & Laws of Indices (for selecting more than one), Download Indices PPQs as WW Powerpoint for Edexcel IGCSE, AQA GCSE, Edexcel GCSE or OCR GCSE (or all GCSE together), Manipulating Formulae/ Changing the Subject, Ratio & Basic Proportion (Including Conversions), Trigonometry Part 2 Identities & Equations, Trigonometry (Part 1) Reciprocal Functions, Notice an error, have a suggestion or any other feedback? endstream (You can unsubscribe at any time.). The plural of index is indices. We can identify it from the way a certain number is written e.g where n is called an exponent/index/power and a is called the base. It's good to establish the laws of indices quickly when learning Indices. During these years I have helped literally hundreds (probably thousands) of students right through from year 3 up to those crucial years of GCSE and A level maths exams. Simplify. 4 3 Simplify the following expression (Level 5) 5254 53 [2 marks] Answer 4 Simplify the following expression. Just like other operations in maths (+, -, x,), Indices are a type of math operations. And best of all they all (well, most!) We get negative indices by dividing two terms with the same base where the first term is raised to a power that is smaller than the power that the second term is raised to. 2 Identify the operation/s being undertaken between the terms. Mixed indices. Express your answer in index form. 2 Flip and change the power from -4 to +4. VuuPGf(x7f E!#yzq5! =(ap4W(JnwWH Check out our website for tons of resources and tips to help you with your assignments. Sometimes the AI can't understand the problem, but, there is a great edit mode for when it makes a mistake, so it is an easy fix. Indices show how many times a number or letter has been multiplied by itself . You should try to carry out the operations in the order that makes the calculation as simple as possible. 1520 Videos, worksheets, 5-a-day and much more Just Maths. Express your answer in index form. x2 x 2 34 3 4 2b1 2 2 b 1 2 We get negative indices by dividing two terms with the same base where the first term is raised to a power that is smaller than the power that the second term is raised to. Average satisfaction rating 4. . Simple rounding worksheets including number lines - Math Salamanders. Since the power is positive, it is a positive index. 4. 3. Includes reasoning and applied questions. K151:Divide Algebraic Terms With Powers. % K438:Determine an Unknown Power e.g. 4 0 obj Ready-to-use mathematics resources for Key Stage 3, Key Stage 4 and GCSE maths classes. Corbettmaths Negative Indices Worksheet (Q1-8) & Solutions Dr Frost resources Dr Frost Video K436: Raise a Number to a Negative Power. ; Work out the value of 64 2/3; Work out all solutions of the equation: 8 m = 2 m 2; Show clearly that 4 3/2 = 8Hence, or otherwise, work out the value of y if 4 y = 8 6; Write down the value of 2 0. Whenever we multiply expressions together with the same index this operation is equivalent to adding the numbers in the index together. Dr Frost Slides & Activities Slides & Worksheet Topic Test Standard Test Extra Questions Dr Frost Questions Key Skills These practice papers are in the same format and style as the real exams, and come in A4 booklets. Question 4:Work out 8^{-\frac{5}{3}} (HIGHER ONLY). Diagrams are NOT accurately drawn, unless otherwise indicated. \begin{aligned} Probability and statistics refresher. corbett maths negative indices. Unformatted text preview: Free GCSE Maths Video Maths Topics Videos Video Topic Video Topic _____ _____ _____ _____ Video 1 Algebraic Fractions Video 9 Indices Video 2 Arcs & Sectors Video 10 Percentages Video 3 BBC BiteSize Video 11 Similar Shapes Video 4 Changing the Subject Video 12 Straight Lines Video 5 Equations & Inequations Video 13 Surds Video 6 Exam Close. 3. Negative Indices Video 175 on www.corbettmaths.com Question 5: Put the expressions above in order, from smallest to largest, when: (a) x = 2 (b) x = 1 (c) x = 0.5 (d) x = 0.5 Work out the 8th term of the sequence. a 5 2 b 7 1 c x 4 x 5 d 9 a 3 3 a 5 e 4 y 12 y 3 f ( ) 2 2 Evaluate, using the calculator. It is mandatory to procure user consent prior to running these cookies on your website. Division (long) Video 19a. pptx, 240.35 KB. This page will give you the 7 easy rules to remember; there are. K433:Laws of Indices for Dividing Powers. Read advice from maths teacher Jo Morgan about helping secondary students understand indices. Corbett Maths offers outstanding, original exam style questions on any topic, as well as videos, past papers and 5-a-day. Increasingly Difficult Exercises: Indices. Negative Indices - Corbettmaths corbettmaths 159K subscribers Subscribe 1.2K 197K views 9 years ago Edexcel Higher Maths Corbettmaths - This video explains how to calculate negative. These cookies do not store any personal information. You may find it helpful to start with the main laws of indices lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Fraction and Ratio Shading. Previous Negative Numbers Answers. A good pass at N5 Maths will set you up well for the fast paced Higher Maths Course next year should you be interested. Dr J Frost (jfrost@tiffin.kingston.sch.uk)@DrFrostMaths . These sessions are free to all University of Sheffield students. Page 5. Primary 5-a-day, videos, worksheets and more A selection of some of my favourite, free maths activities to use in lessons. 3x3 cube how to solve Can delta h be negative Construction calculator pro free download Cube faces edges corners How to find rank of a matrix in r How to study for math How to write a root as an exponent How to write an exponential function whose graph passes through points How wide is 5mm in inches Math finding angles Modular system of . Rounding spiders - alutwyche on TES. &=3 \times \frac{b^{-2}}{1} all (well, most!) 38 = 2 8 3 = 2 Then, as the numerator is 2 we then square the answer. The thermometer below shows the temperature at 6am in a town The temperature increases by 7C by 10am Corbettmaths 2018 Diagrams are NOT accurately drawn, unless otherwise indicated. Your personal data will be used to support your experience throughout this website, to manage access to your account, and for other purposes described in our privacy policy. Increasingly Difficult Exercises: Fractional and Negative Indices Increasingly Difficult Exercises: Solving Equations with Indices Dr Frost: Sherlocked - Laws of Indices Dr Frost: Law of Indices Head to Head Alutwyche: Defuse the bomb indices Alutwyche: Simplifying Indices Match Up Alutwyche: Indices Codebreakers Corbett Maths offers outstanding, original exam style questions on any topic, as well as videos, past papers and 5-a-day. This video shows a guide to indices and powers. software yourself. Previous Distance Time Graphs Practice Questions. The base number is 3 and is the same in each term. % (a) The n th term of a sequence is 2 n + 2 n + 1. Step 2: Determine the index type. 5-a-day GCSE 9-1; 5-a-day Primary; 5-a-day Further Maths; 5-a-day GCSE A*-G; 5-a-day Core 1; More. What are Indices? Indices Worksheets Example 2. 4 x 24 in distributive property - Write 4x24 as distributive property 44 people found it helpful 4 x 24 = 4 x 20 = 40 4 x 4 = 16 40 + 16 = 56 4 x 24 = 56 Need Menu Skip to content. This website uses cookies to improve your experience while you navigate through the website. x2 x 2. In other words, the rule can also be written as, \textcolor{red}{a}^{\large{\frac{\textcolor{blue}{b}}{\textcolor{limegreen}{c}}}} = (\sqrt[\textcolor{limegreen}{c}]{\textcolor{red}{a}})^\textcolor{blue}{b}. No fees, no trial period, just totally free access to the UKs best GCSE maths revision platform. Information Examples, solutions, and videos to help GCSE Maths students learn about negative and fractional indices. So clearly, a -1 = In same way, a -2 = = a -3 = = Thus, we have written the expression as a power of 3. we can follow the steps as outlined above. Pythagoras' Theorem (Corbett Maths). 10. in accordance with our Cookie Policy. K436:Raise a Number to a Negative Power. Prepare your KS4 students for maths GCSEs success with Third Space Learning. Simplify. The fractional indices laws apply when the power is a fraction. Using the powers law of indices . New Further Maths. We can read this as 4 to the power 3. Learn more today with the MME GCSE Maths flashcards. Worksheets with answers . GCSE Revision. Example 1: Negative Powers Simplify the following, 4^ {-3} 43. There are two roots when calculating the square root of a number (a positive and a negative solution). Lots of credit goes to her for resources and ideas used in these lessons. 2. Answer the Questions in the spaces provided there may be more space than you need. Focus your time on the mistakes and misconceptions of your students and give them the feedback to improve. Further Maths 1; Further Maths 2; Extension Questions; A Level Practice Papers 2019 Specs; Tuition; Select Page. Negative Numbers Questions Worksheets; Post navigation. Get a closer look with this tutorial! and 5-a-day. augusta national greenskeeper salary; baby bonnet pattern crochet; cyberlink screen recorder deluxe; corbett maths negative indiceswho plays jennifer in black lightningwho plays jennifer in black lightning The worksheets are designed in landscape so they can be conveniently displayed on screen, as well as printed. 4. &a(2 b)^{-4}\\ Fire up KS2 pupils' imagination with this collection of 16 fictional stories, written by literacy expert Pie Corbett. K692:Raise a Fraction to a Fractional and Negative Power. 2b1 2 2 b 1 2. There are few better places to your own . 3. Raising a term to the power of 3 means we cube it. View all students answers, scores and comments and hold them accountable for their effort. &=\frac{3^{2}}{4^{2}} \\\\ Interactive tools and activites to aid the teaching of mathematics. Number Algebra Ratio Measurement Geometry Probability Statistics Sets Calculus. Powers of quotients. Dividing by 10, 100, 1000 Video 18 Questions Answers. GCSE Edexcel Maths Revision Number Negative and Fractional Indices Addition and Subtraction Algebra Factorising Harder Questions Coordinates Ratio . ]_f%C$@$@!B`EWMLJF}+4V_|XD5jX7H$@$@@ #^J7mD_ #HH$@$@AI ;6lCAU)SIHeZzY;iPL&8/GF3$@$@!N k)l7+/us1@2L> .gbl?t7,K63IK||? Negative indices are powers (also called exponents) with a minus sign in front of them. N6a Using powers and roots. Given we know that \sqrt4=2 , this becomes. K440: Raise an Algebraic Term to a Negative Power. Higher Phase Weekly 'Corbett Maths 5-a-day' check ins perpendicular line equation to find the value of c. Get Help with Homework Looking for someone to help with your homework? Indices - Videos 172, 174. The plural word for index is indices. This is the students version of the page. Homework Support Solutions. Example 3: Simplify $$\frac{\left(3x^2y^2\right)^2\times\left(4xy\right)^3}{24x^4y^7}$$. %PDF-1.3 GCSE (1 - 9) Fractional and Negative Indices Name: _____ Instructions Use black ink or ball-point pen. A worksheet on Negative Numbers. 3 \times \frac{b^{-2}}{1} &=3 \times \frac{1}{b^{2}} \\ Maths Drills. Level 5 - Evaluating indices expressed as fractions. Factors Video 22 Questions Answers. One to one maths interventions built for KS4 success, Weekly online one to one GCSE maths revision lessons now available. Dont worry weve also included an answer sheet in the download. Sign up for free, Negative and fractional indices worksheet GCSE maths resource with answers. xXn6}WL@#}khq@Q}p;qu$vNj&%/\I-lw~'VvEi~"&)^@6> M@7R+/O+U-SSRZA^*A]S $^b0m1:BKCM(&+t7. Multiply and divide using index laws. Welcome; Videos and Worksheets; Primary; 5-a-day. 3. Indices Rule 10: Negative Powers. Questions. Simplify. Adding and Subtracting with Negative Numbers Practice Strips ( Editable Word | PDF | Answers) Multiplying and Dividing with Negative Numbers Practice Strips ( Editable Word | PDF | Answers) Mixed Operations with Negative Numbers Practice Strips ( Editable Word | PDF | Answers) NEGATIVE INDICES Materials required for examination Items included with question papers Ruler graduated in centimetres and Nil millimetres, protractor, compasses, pen, HB pencil, eraser. Q2. Revise about how to multiply and divide indices, as well as apply negative and fractional rules of indices with this BBC Bitesize GCSE Maths Edexcel Laws of indices. When we cancel the common factors of x. I have tried out each and every one with my students. It's good to establish the laws of indices quickly when learning Indices. Great, I aced Math, say goodbye to hard maths questions, always accurate. But opting out of some of these cookies may affect your browsing experience. stream Solutions. Good level of challenge + lots of misconceptions drawn out. The negative index number means we need to find the reciprocal, so. (Level 5) 255 53 [2 marks] Answer Turn over for docx, 11.59 KB. There are a number of important rules of index numbers: y a y b = y a+b; Examples. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. Read each question carefully before you begin answering it. For instance, $$a^{-2}$$, $$b^{-5}$$. Basics, Indices Rules - 5 0 obj Factors Video 22 Questions Answers. An index number is a number which is raised to a power. We also use third-party cookies that help us analyze and understand how you use this website. Area and Circumference of Circles. exam style questions on any topic, as well as videos, past papers Good luck! As it is a negative power we can rewrite this as, 8^{-\frac{5}{3}}=\frac{1}{8^{\frac{5}{3}}}. K149:Multiply Algebraic Terms With Powers. (Up to 0:34), Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost (Ignore Numerator not 1), Corbett Maths Fractional Indices (From 2:41). Thus, we have written the expression as a power of 2. I have tried In Q9 they need to write examples in index form. >> /Font << /F1.0 8 0 R /F1.1 11 0 R /F2.0 9 0 R /F3.0 10 0 R >> /XObject square rooting has the effect of halving the power. true /ColorSpace 22 0 R /Intent /Perceptual /SMask 23 0 R /BitsPerComponent p k 93d_C81Y2FEk)(LO+KCdGv\7jGWmNX}l\ Corbett Maths offers outstanding, original exam style questions on any topic, as well as videos, past papers and 5-a-day. The power, also known as the index, tells you how many times you have to multiply the number by itself. . 34 3 4. Equations Video 21 Questions Answers. Welcome to MathsDIY. For instance, in $$10^{\frac{7}{9}}$$, $$9^{\text{th}}$$ the root of $$10$$ is multiplied $$7$$ times. K437:Raise a Fraction to a Negative Power. 4. Example 1: Express $$\left(\sqrt[4]{8}\right )^6$$ in the form of $$a^\frac{m}{n}$$. We can provide expert homework writing help on any subject. 10/10 app, would highly recommend. GCSE Higher. The following diagrams show fractional indices and how to evaluate them. Then remember that multiplying a positive number by a negative number gives a negative, so the answer is: 2 4 4 = 9 6. &=\frac{9}{16} << /Type /Page /Parent 3 0 R /Resources 6 0 R /Contents 4 0 R /MediaBox [0 0 595 842] Prerequisites. We get negative indices by dividing two terms with the same base where the first term is raised to a power that is smaller than the power that the second term is raised to. %PDF-1.3 Inequality Practice Questions Answers Textbook Answers 177. Indices Worksheets Example 2. Fractional indices: If the index of a number is in fractional form, then it is termed fractional indices. Next in this negative and fractional indices worksheet theres some reasoning activities with fill-in-the-blanks style questions (Q7). It's good to establish the laws of indices quickly when learning Indices. Previous Cube Roots Video. Find out more about our GCSE maths revision programme. Answers. These are the temperatures in towns cities on the same day. This worksheet was automatically generated by the DrFrostMaths . Axioms and arrays. K767:Use Change of Base to Form a Linear Formula. 2023 Third Space Learning. So, we know that 9^{\frac{3}{2}} is equal to \sqrt[2]{9^3} or (\sqrt[2]{9})^3. We then begin to mix negative and fractional indices across Q5-6. Notice that in this example we chose to perform the \sqrt{4} operation before cubing the answer. Below is an example of a term written in index form: 4 3 4 3. 2. Corbett maths trigonometry worksheet. After studying this section, you will be able to: divide and multiply algebraic expressions using indices. Answer the questions in the spaces provided Information The marks for each question are shown in brackets Interactive Resources . Zero indices: If the index of any number is zero, then it is termed a zero index. Lower = 47.5 Upper = 48.5 Edges, Faces, Vertices Video 20 Questions Answers. Series of slides, questions/examples/starters I have used recently on negative/fractional indices. 22 = 4 2 2 = 4 So, Guaranteed Originality. It really is one of the very best websites around. xYMs7W(I'&4(N8>vW*r=RK@_/QwZN[yFDooFA(2FN6xbu3am xCu+C6?d;:ZQ]Kb+:CGdw* ]c|2d0~`D@)ic2)cdB pLnc*2Nfh K432:Laws of Indices for Multiplying Powers. Determine math questions. \bigg(\dfrac{\textcolor{blue}{a}}{\textcolor{limegreen}{b}}\bigg)^{-\textcolor{red}{x}} = \bigg(\dfrac{\textcolor{limegreen}{b}}{\textcolor{blue}{a}}\bigg)^\textcolor{red}{x}, We now know that 4^{-3} is equal to \dfrac{1}{4^3}. << /Length 5 0 R /Filter /FlateDecode >> Other lessons in this series include: To make the negative index positive we put the term over 1 and flip it. Division. I have big plans for Blacksmith Maths. For Free. Diagrams are NOT accurately drawn, unless otherwise indicated. Hes the author of Visible Maths and Conceptual Maths (Crown House Publishing). Page 7. Increasingly Difficult Exercises: Negative Indices. << /Length 5 0 R /Filter /FlateDecode >> The first part of the expression is a power of 2, whilst the second part is a power of 8. By clicking continue and using our website you are consenting to our use of cookies Set personalised, comprehensive and scaffolded work quickly from your markbook. Worksheet Name 1 2 3 Indices Rules - Basics 1 2 3 Indices Rules - Advanced 1 2 3 Corbett Maths keyboard_arrow_up Back to Top Corbett Maths offers outstanding, original exam style questions on any topic, as well as videos, past papers and 5-a-day. 2 stars (the app is worth 5 but because of that now after editing you get 4) because of that stupid way you implemented the premium feature , I mean adding a premium mode to your app is perfectly okay if you add new features and then asking for money but taking something old and asking for money for that is complete laziness and lack of interest from the . A Level Revision . 5-a-day Further Maths; 5-a-day GCSE A*-G; 5-a-day Core 1; More. 110. (You can unsubscribe at any time.). Most popular sequences Nth term of a linear sequence spider Changing the subject of a formula (6 exercises) Solving linear equations spider Upper and lower bounds with significant figures Applying the rules of indices to form and solve equations Advert Categories A Level Binomial expansion Complex numbers Differentiation Functions Integration - Convert numbers from standard form with negative powers into ordinary numbers. Fractional and negative indices - Help for AQA Maths Mod 3 Higher Show Step-by-step Solutions. Raising a term to the power of means we find the square root of it. The plural of index is indices. &=\frac{1}{16 b^{4}} A Level Papers . Next Negative Indices Practice Questions. How to solve negative indices. It helps me solve math problems , i would definitely recommend people who are struggling with maths, thanks to the developers for keeping it mostly free. The marks for each question are shown Corbett Maths offers outstanding, original exam style questions on any topic, as well as videos, past papers and 5-a-day. Get your free negative indices worksheet of 20+ questions and answers. In general, the result of a negative power is \bf{1} over that number to the positive power, i.e. Passing N5 Maths significantly increases your career opportunities by helping you gain a place on a college course, apprenticeship or even landing a job. Math Index. 2. Fractional and Negative Indices Name: _____ Instructions Use black ink or ball-point pen. Brackets with indices. Negative indices are powers (also called exponents) with a minus sign in front of them. Express your answer in index form. It's really good for doing problems fast and easy. Maths revision video and notes on the topic of Negative and Fractional Indices. Last modified: 9th July 2021. Recap of Fractional and Negative Indices with 2 sets of differentiated "Super 9" practice questions. << /Length 5 0 R /Filter /FlateDecode >> The Textbook Exercise on Negative Indices. Name: Exam Style Questions Ensure you have: Pencil, pen, ruler, protractor, pair of compasses and eraser You may use tracing paper if needed Guidance All lessons I create I use myself as well as share to my own department. So, to work out (\sqrt[2]{9})^3, we first have to square root 9, which is easy enough the square root of 9 is 3. A great thankx to This app inc. Thus, the simplified value of $$\frac{\left(3x^2y^2\right)^2\times\left(4xy\right)^3}{24x^4y^7}$$ is $$24x^3$$. There are other names for an index, including power and also logarithm. Name. Positive indices: If the index of any number is a whole number, then it is termed as a positive index. After studying this section, you will be able to: divide and multiply algebraic expressions using indices. 3C;Srg;C>c)e +h Check your answers seem right. So, (\sqrt[2]{9})^3 becomes 3^3, which is, Write 2^{15}\times 8^{-4} as a power of 2, and hence evaluate the expression. b) Perform the calculation as if the numbers were positive: Worksheets with answers . Q3 in this excellent resource covers unit fractional indices to all of these types of numbers, before bringing in non-unit fractional indices in Q4. Indices Worksheets Example 2 It's good to establish the laws of indices quickly when learning Indices. File previews. The temperature in Watford is 9C colder than Redtown Towns Temperature Leek -8C 3. Question 2: Work out \sqrt{9}\times 6^{-2}, Write your answer in its simplest form (Non-calculator), Firstly, as 3^2=9, the inverse operation gives, \sqrt{9}=3. For instance, $$2^{4}=2\times 2\times 2\times 2$$. DrFrostMaths.com GCSE Laws of Indices KS3/4 :: Number :: Powers, Roots & Laws of Indices Covers laws of indices (including fractional and negative indices), solving equations involving indices (IGCSE FM syllabus) and raising a single term to a power.