Negative and Fractional indices | Teaching Resources Negative and Fractional indices Subject: Mathematics Age range: 14-16 Resource type: Unit of work 8 reviews File previews pptx, 1.48 MB Series of slides, questions/examples/starters I have used recently on negative/fractional indices. Next consider mixed numbers and decimals. Increasingly Difficult Exercises: Fractional Indices. . Set personalised, comprehensive and scaffolded work quickly from your markbook. Directed Number. For instance, $$2^{4}=2\times 2\times 2\times 2$$. Diagrams are NOT accurately drawn, unless otherwise indicated. September 2, 2019 corbettmaths. GCSE: (b) Deal with fractional exponents. 3. \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? There are daily questions found at www.corbettmathsprimary.com/5-a-day/ 1. stream \textcolor{red}{64}^{\large{\frac{\textcolor{limegreen}{2}}{\textcolor{blue}{3}}}}= \sqrt[\textcolor{blue}{3}]{\textcolor{red}{64}^\textcolor{limegreen}{2}}, \sqrt[\textcolor{blue}{3}]{\textcolor{red}{64}} = \textcolor{red}{4}, \textcolor{red}{4}^\textcolor{limegreen}{2} = \textcolor{red}{16}, Negative powers flip the fraction and put 1 over the number. for any value of a or b. 1. Menu Skip to content. Write 0.08 as a fraction. Example 2: Determine if 7^2\times 7^ {-6} 72 76 has a positive, negative or zero index. The power, also known as the index, tells you how many times you have to multiply the number by itself. Level 2 Certificate in Further Mathematics. Section B: Higher GCSE and easier A-level. GCSE Edexcel Maths Revision Number Negative and Fractional Indices Addition and Subtraction Algebra Factorising Harder Questions Coordinates Ratio . endobj It's good to establish the laws of indices quickly when learning Indices. Welcome; Videos and Worksheets; Primary; 5-a-day. 12 0 obj Equations Video 21 Questions Answers. &=\frac{3}{b^{2}} Answer the questions in the spaces provided there may be more space than you need. Radio 4 podcast showing maths is September 2, 2019 corbettmaths. Brackets with indices. I have also included a BINGO activity to recap basic laws of indices before moving onto the more difficult content. In general, the result of a negative power is \bf{1} over that number to the positive power, i.e. VuuPGf(x7f E!#yzq5! =(ap4W(JnwWH (c) Deal with problems involving a mixture of bases. For example, 2 5 means that you have to multiply 2 by itself five times = 22222 = 32. Q2. Negative exponents will often be used in conjunction with other index laws, including the division, brackets and multiplication laws. 3. 4 0 obj 110. This is commonly use to show square and cube roots. worksheet, complete with answers. 6 0 obj For instance, $$a^{-2}$$, $$b^{-5}$$. Raising a term to the power of means we find the cube root of it. \end{aligned}\], \[\frac{\left(\frac{2}{3}\right)^{-2}}{1}\], \[\frac{1}{\left(\frac{2}{3}\right)^{2}}\], \[\frac{1}{\left(\frac{2}{3}\right)^{2}}=\frac{1}{\frac{2^{2}}{3^{2}}}=\frac{1}{\frac{4}{9}}\], \[\frac{1}{\frac{4}{9}}=1 \div \frac{4}{9}=1 \times \frac{9}{4}=\frac{9}{4}\], \[\left(\frac{2}{3}\right)^{-2}=\left(\frac{3}{2}\right)^{2}=\frac{3^{2}}{2^{2}}=\frac{9}{4}\]. E.g. Step 1: Recall the formula $$a^{m}\times a^{n}=a^{m+n}$$. 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 . Download all files (zip) GCSE-Indices.pptx (Slides) GCSE-LawsOfIndices.pdf (Worksheet) Types of Numbers. K689:Raise a Number to a Fractional Power. No fees, no trial period, just totally free access to the UKs best GCSE maths revision platform. endobj JX. - Multiply and divide numbers in standard form. Videos, worksheets, 5-a-day and much more Examples, solutions, videos, activities and worksheets that are suitable for A Level Maths to help students learn the multiplication rule, division rule and power rule of indices. Find how many yellow sweets are in the packet. 4. Mistry Maths: Powers multiplying and dividing ; 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. Learn more today with the MME GCSE Maths flashcards. 8 /Filter /FlateDecode >> Negative Fractional Indices - Go Teach Maths: Handcrafted Resources for Maths Teachers From your 'My Account' page, you can give feedback, change I have tried out each and every one with my students. For instance, $$2^4$$, $$a^5$$. 34 3 4. 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. There are other names for an index, including power and also logarithm. The following diagrams show fractional indices and how to evaluate them. K690:Raise a Number to a Fractional and Negative Power. Indices - Videos 172, 174. many years. Division (short) Video 19 Questions Answers. . There are few better places to your own Blog Post Reads, Links to the Best Maths Answer all questions. So, we get that 4^ {-3}=\frac {1} {64} 43 = 641. We found that Corbettmaths.com is moderately 'socialized' in respect to Twitter mentions (37.5K), Facebook shares (676) and Google+ shares (4). For instance, in $$10^{\frac{7}{9}}$$, $$9^{\text{th}}$$ the root of $$10$$ is multiplied $$7$$ times. Increasingly Difficult Exercises: Negative Indices. Negative Indices Textbook Answers - Corbettmaths. I have big plans for Blacksmith Maths. Probability and statistics refresher. Negative powers can be explained by extending the division law (ie what happens when we divide b 2 by b 7 ? By clicking continue and using our website you are consenting to our use of cookies Whenever we multiply expressions together with the same index this operation is equivalent to adding the numbers in the index together. 3 b^{-2} &=3 \times b^{-2} \\ The plural of index is indices. The laws of indices Introduction A power, or an index, is used to write a product of numbers very compactly. It's really good for doing problems fast and easy. Where pupils have these pre-requisite skills, we recommend adapting the questions (where appropriate) to include this content. 100% Free. You should try to carry out the operations in the order that makes the calculation as simple as possible. Laws of indices as applied to products. Simplify the following, 9^{\frac{3}{2}}. Corbett Maths offers outstanding, original exam style questions on any topic, as well as videos, past papers and 5-a-day. Whenever we multiply expressions together with the same index this operation is equivalent to adding the numbers in the index together. Simplify 3 2 3 3. On most occasions the positive root is the only one required. Step 2: Determine the index type. Corbettmaths Videos, worksheets, 5-a-day and much more. Links to the Best Maths Websites in the World, AQA Level 2 Certificate in Further Mathematics, Indices Rules - Given we know that \sqrt4=2 , this becomes. Guaranteed Originality. Look out for the laws of indices worksheets and exam questions at the end. No products in the cart. 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. K693: Raise an Algebraic Term to a Fractional Power. Circles. I have tried Maths : Indices - Introduction. Tables. \textcolor{red}{x}^{\large{\frac{\textcolor{limegreen}{1}}{\textcolor{blue}{2}}}}= \sqrt[\textcolor{blue}{2}]{\textcolor{red}{x}^\textcolor{limegreen}{1}} =\sqrt[\textcolor{blue}{2}]{\textcolor{red}{x}}, \textcolor{red}{x}^{\large{\frac{\textcolor{limegreen}{1}}{\textcolor{blue}{3}}}}= \sqrt[\textcolor{blue}{3}]{\textcolor{red}{x}^\textcolor{limegreen}{1}} =\sqrt[\textcolor{blue}{3}]{\textcolor{red}{x}}, Note: it doesnt matter which order you carry out the square root and multiplication operations. Q6 explictly asks for a surd form. 5 0 obj Corbett Maths Equations with Indices (From 6:19), Maths By Fives Exponential Equations Examples. Equations with Indices. GCSE: (b) Deal with fractional exponents. Level 9 GCSE Maths Papers 2022 are designed for students who want to achieve the top grades in their GCSE Maths exam. Practice Questions. a) Perform the calculation as if the numbers were positive: 2 4 4 = 9 6. When y = 18.3 then x = 3. The farmer must pay 1p tax for each m 2 of land he owns. a means "a" squared which means "a" multiplied by "a". Example 2: Determine if $$7^2\times 7^{-6}$$ has a positive, negative or zero index. Read each question carefully before you begin answering it. The Negative index. To help us show you teaching resources, downloads and more youll love, complete your profile below. \begin{aligned} Level 4 - Multiplying, dividing and raising to another power. &a(2 b)^{-4}\\ (You can unsubscribe at any time.). The fractional indices laws apply when the power is a fraction. Using the powers law of indices . Answer all questions. The profit from each revision guide is reinvested into making free content on MME, which benefits millions of learners across the country. Indices show how many times a It really is one of the very best websites around. 2 3-2 = k. 3 3-4 = l. 25 10-4 = 2. Maths revision video and notes on the topic of Negative and Fractional Indices. Good level of challenge + lots of misconceptions drawn out. Fractional and Negative Indices Name: _____ Instructions Use black ink or ball-point pen. \textcolor{red}{a}^{-\textcolor{limegreen}{b}} = \dfrac{1}{\textcolor{red}{a}^\textcolor{limegreen}{b}}. am an = amn a m a n = a m n. Step-by-step guide: Dividing indices. Categorisation: Identify a missing power when negative indices are involved. Example 1: Negative Powers Simplify the following, 4^ {-3} 43. (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. 22 = 4 2 2 = 4 So, 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}}. Write an equation for y in terms of x. Students need to use their powers of reasoning to explain why theyre seeing the results they are. TES Maths Resources Collections, AQA negative_indices_answer_sheet.pdf. These cookies will be stored in your browser only with your consent.
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