worksheet, complete with answers. Necessary cookies are absolutely essential for the website to function properly. Textbook Exercise Previous Laws of Indices (numerical) Textbook Exercise Next Inequalities Textbook Exercise Thus, the simplified value of $$\frac{\left(3x^2y^2\right)^2\times\left(4xy\right)^3}{24x^4y^7}$$ is $$24x^3$$. September 11, 2016 corbettmaths. So, that leaves 6^{-2}, this becomes the following fraction, Multiplying our two answers together, we get, \sqrt{9}\times 6^{-2}=3\times\dfrac{1}{36}=\dfrac{3}{36}=\dfrac{1}{12}, Question 3: Work out 4^{\frac{1}{2}}\times4^{\frac{3}{2}}. K440:Raise an Algebraic Term to a Negative Power. Simplify. (Level 5) 255 53 [2 marks] Answer Turn over for docx, 11.59 KB. The profit from each revision guide is reinvested into making free content on MME, which benefits millions of learners across the country. This Writing equations of parallel and perpendicular lines answers provides step-by-step instructions for solving all math problems. What are Indices? Since the power is positive, it is a positive index. Positive indices: If the index of any number is a whole number, then it is termed as a positive index. 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. 3 b^{-2} &=3 \times b^{-2} \\ You also have the option to opt-out of these cookies. I have been a Tarsia fan for (3m^2)^4 = 81m^8. This worksheet features converting negative indices into fractions and vice-versa as well as converting decimals into index notation. You must show all your working out. However, the fraction needs to be simplified further. Everything you need to get an A+ in IGCSE, GCSE and O-Level Maths. 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. Laws of Indices: Worksheets with Answers. The Corbettmaths Practice Questions on Negative Indices for Foundation GCSE Maths. The power, also known as the index, tells you how many times you have to multiply the number by itself. Whether you want a homework, some cover work, or a lovely bit of extra practise, this is the place for you. authorised service providers may use cookies for storing information to help provide you with a Lower = 47.5 Upper = 48.5 Edges, Faces, Vertices Video 20 Questions Answers. Websites in the World, My 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. GCSE: (b) Deal with fractional exponents. 2 0 obj >> /Font << /F1.0 8 0 R /F1.1 11 0 R /F2.0 9 0 R /F3.0 10 0 R >> /XObject Brackets with indices. Super amazing I am a student in math and this will get me higher grades for sure I will definitely recommend this. Learn more today with the MME GCSE Maths flashcards. Further Maths; Practice Papers; Conundrums; Class Quizzes; Blog; About; Revision Cards; Books; March 24, 2013 August 20, 2019 corbettmaths. Fractional and Negative Indices Name: _____ Instructions Use black ink or ball-point pen. The terms are being multiplied. So clearly, a -1 = In same way, a -2 = = a -3 = = "Full Coverage": Laws of Indices This worksheet is designed to cover one question of each type seen in past papers, for each GCSE Higher Tier topic. Corbettmaths - This video goes through the laws of indices needed for both the foundation and higher tiers. There are few better places to your own Menu Skip to content. << /Im1 12 0 R /Im5 20 0 R /Im4 18 0 R /Im2 14 0 R /Im3 16 0 R >> >> )6#IF=3JouECnWXFQ)YE-,^_Qf7E9nGovAHKVA*@p(, pccQd22i-6B&L1+eFf&c@&1V:&4UOv0~ah8y1k]#]rg 2. Just like other operations in maths (+, -, x,), Indices are a type of math operations. Hes the author of Visible Maths and Conceptual Maths (Crown House Publishing). So, $$2$$ is the base and $$4$$ is the index. Answer the questions in the spaces provided there may be more space than you need. &a(2 b)^{-4}\\ Level 1 - Evaluating positive indices without a calculator. It really is one of the very best websites around. Corbett Maths offers outstanding, original Past Paper Questions by Topic. Rich Tasks . The Corbettmaths Practice Questions on Fractional and Negative Indices for Level 2 Further Maths. View All Tables. O7*;I*$jn?=(IHKC11Q'?MFf9Cl5NnS: @h0<2-^}i2*==M>m?mMzH$@$@XfMjjOkko/hUlu4I# 8 NuBRbw'wL3g0E.Uc GCSE Papers . and 5-a-day. The laws of indices Introduction A power, or an index, is used to write a product of numbers very compactly. Next in this negative and fractional indices worksheet theres some reasoning activities with fill-in-the-blanks style questions (Q7). 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 . Answer all questions. This is why when dealing with fractions it is easier to skip to step 2 and just flip the fraction: 1. Example 1: Determine if $$5^4\times 5^3$$ has a positive, negative or zero index. TES Maths Resources Collections, AQA %PDF-1.3 Clear up mathematic question 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. tying off loose ends knitting 0.00 Cart. One to one maths interventions built for KS4 success, Weekly online one to one GCSE maths revision lessons now available. 100% Free. Negative Indices (Foundation) - Practice Questions - Corbettmaths. Using the powers law of indices . For instance, $$2^4$$, $$a^5$$. Averages and Range. Hundreds of randomly generated questions and answers. CORBETTMATHS 2018. extra practise, this is the place for you. Any cookies that may not be particularly necessary for the website to function and is used specifically to collect user personal data via analytics, ads, other embedded contents are termed as non-necessary cookies. Get what you need to become a better teacher with unlimited access to exclusive free classroom resources and expert CPD downloads. (b) The n th term of a different sequence is 9 ( 3 n + 3 n + 1) Expand and express this expression as the sum of two powers of three. When dividing indices with the same base, subtract the powers. Negative exponents will often be used in conjunction with other index laws, including the division, brackets and multiplication laws. Primary 5-a-day, videos, worksheets and more A selection of some of my favourite, free maths activities to use in lessons. Dividing indices. Follow Peter on Twitter at @MrMattock. - Multiply and divide numbers in standard form. 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 Homework Help Online. Try the free Mathway calculator and problem solver below to practice various math topics. Corbett Maths offers outstanding, original exam style questions on any topic, as well as videos, past papers and 5-a-day. Step 1: Recall the laws of indices that has to be used, Step 2: Simplify the numerator of the expression, Step 3: Simplify the denominator of the expression, Thus, $$\frac{h^{-3}\times h^{6}}{h^5\times h^{-3}}=h$$. Read each question carefully before you begin answering it. favourite authors. Two roots could be written. A Level Papers . Contact me at westiesworkshop@gmail.com, 3.3 Fractional Powers numerator not 1, possibly negative, Whole Topic Summary Resources (Including Past Paper Questions), Powers and Roots (Integer Powers) Topic Review, Powers and Roots (Fractional & Negative Indices) Topic Review, Simplify to powers of 3 or 5, then apply laws of indices, Powers and Roots (Change of Base) Topic Review, Investigating Algebraic Powers Activity (, Simplifying Using Power Laws Practice Strips (, Simplifying Expressions Involving Brackets and Powers (, Fractional and Negative Indices True or False (, Negative & Fractional Indices AQA Level 2, Powers and Roots Revision Practice Grid (, Equations Involving Indices/Roots AQA Level 2. Indices GCSE Maths Revision Higher Level Worked Exam Questions (include fractional and negative powers) Examples: Work out 56 1 - 56 0; Explain why 27 1/3 = 3; Write 27-1/3 as a fraction. (b) Be able to raise a whole term to a power, e.g. Laws of indices as applied to products. 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. \end{aligned}\], \[\left(\frac{4}{3}\right)^{-2}=\left(\frac{3}{4}\right)^{2}\], \[\begin{aligned} Home; Videos and Worksheets; 5-a-day; Study Cards; Practice Papers; July 31, 2018 July 31, 2018 corbettmaths. 4 (no answers), Increasingly Questions. An index, or power, is the small floating number that appears after a number or letter. << /ProcSet [ /PDF /Text /ImageB /ImageC /ImageI ] /ColorSpace << /Cs1 7 0 R Posts about Worksheets written by corbettmaths. Indices or powers are used to write statements involving repeated multiplication in shorthand. 5-a-day Further Maths; 5-a-day GCSE A*-G; 5-a-day Core 1; More. E.g. engaging lesson activity, then you have come to the right place! 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. When the power is \textcolor{blue}{-1}, this takes the form, \textcolor{red}{a}^{\textcolor{blue}{-1}}=\dfrac{1}{\textcolor{red}{a}} or \textcolor{red}{10}^{\textcolor{blue}{-1}} = \dfrac{1}{\textcolor{red}{10}}. right!? Multiplication Grids. JX. GCSE Maths Predicted Papers are perfect for preparing for your GCSE Maths exams. Sign up for free, Negative and fractional indices worksheet GCSE maths resource with answers. endobj We found that Corbettmaths.com is moderately 'socialized' in respect to Twitter mentions (37.5K), Facebook shares (676) and Google+ shares (4). Fractions: Adding (same denominators) Video 23 Questions Answers. K434:Laws of Indices for Raising a Power to a Power. If some number is raised to some power, then the power it is raised to is the index of that number. The rules make complex calculations that involve powers. \end{aligned}, \left(\frac{5}{8}\right)^{-1}=\frac{8}{5}, \left(\frac{8}{125}\right)^{-\frac{2}{3}}, We use essential and non-essential cookies to improve the experience on our website. Solutions. \textcolor{red}{a}^{\textcolor{blue}{-1}}=\dfrac{1}{\textcolor{red}{a}}, \textcolor{red}{10}^{\textcolor{blue}{-1}} = \dfrac{1}{\textcolor{red}{10}}, Go back to the main GCSE Maths topic list, Mon - Fri: 09:00 - 19:00, Sat 10:00-16:00, Not sure what you are looking for? Find out more about our GCSE maths revision programme. The sweets are all red, yellow or green in the ratio of 4 : 2 : 3.
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