# Indices

## A self marking exercise on indices including evaluating expressions and solving equations.

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This is level 3: evaluating negative and zero indices. You will be awarded a trophy if you get at least 18 correct and you do this activity online.
Simplify the following.

 $$2^0$$ $$1^{-1}$$ $$2^{-1}$$ $$1^{-2}$$ $$1^0$$ $$2^{-2}$$ $$3^0$$ $$15^0$$ $$5^{-3}$$ $$10^{-2}$$ $$4^{-1}$$ $$10^{-3}$$ $$5^{-1}$$ $$2^{-3}$$ $$5^{-2}$$ $$\left(\dfrac{1}{7}\right)^{-1}$$ $$\left(\dfrac{1}{19}\right)^{-1}$$ $$\left(\dfrac{1}{5}\right)^{-2}$$ $$\left(\dfrac{5}{2}\right)^{-1}$$ $$\left(\dfrac{5}{3}\right)^{-2}$$ $$\left(\dfrac{10}{7}\right)^{-3}$$
Check

This is Indices level 3. You can also try:
Level 1 Level 2 Level 4 Level 5 Level 6 Level 7 Level 8 Level 9

## Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

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## Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

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Saturday, August 22, 2020

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Scan the QR code below to visit the online version of this activity.

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## Description of Levels

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Level 1 - Evaluating positive indices without a calculator

Level 2 - Evaluating positive indices with a calculator

Level 3 - Evaluating negative and zero indices

Level 4 - Multiplying, dividing and raising to another power

Level 5 - Evaluating indices expressed as fractions

Level 6 - Mixed questions involving integer, negative and fractional indices

Level 7 - Multiplying, dividing and raising to another power with coefficients

Level 8 - Solving simple equations involving indices

Level 9 - Solving interesting equations involving indices

Indices Challenge - Dr Tim Honeywill has come up with these challenges to test your understanding of indices and algebra.

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

Game - Find the matching pairs of indices in this interactive online game.

Laws of Indices - a drag-and-drop true/false challenge.

More Indices including lesson Starters, visual aids, investigations and self-marking exercises.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

## Examples

 52 = 5 x 5 = 25 53 = 5 x 5 x 5 = 125 54 = 5 x 5 x 5 x 5 = 625 51 = 5 50 = 1 5-1 = 1⁄5 5-2 = 1⁄5x5 = 0.04 5a × 5b = 5a+b 5a ÷ 5b = 5a-b (5a)b = 5ab

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

### Typing Mathematical Notation

These exercises use MathQuill, a web formula editor designed to make typing Maths easy and beautiful. Watch the animation below to see how common mathematical notation can be created using your keyboard.

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