# Power Play

## Exercises on powers and roots and simplifying index expressions involving numbers of the same base.

##### Menu  Level 1Level 2Level 3Level 4Level 5Level 6Level 7  Help    More

This is level 5: the second law of indices with numbers. You will be awarded a trophy if you get at least 5 answers correct and you do this activity online.

Simplify the following using the caret symbol (^) on your keyboard to show indices. For question 6 use the button for the multiplication sign and give products of powers in ascending order of their bases.

 1 $$2^7 \div 2^3$$as a power of 2 ☐= ☐ ✓ ✗ 2 $$8^{20} \div 8^{17}$$as a power of 8 ☐= ☐ ✓ ✗ 3 $$5^4 \div 5^4$$as a power of 5 ☐= ☐ ✓ ✗ 4 $$5^4 \div 5^4$$as a single digit number ☐= ☐ ✓ ✗ 5 $$7^{12} \div 7^5 \div 7$$as a power of 7 ☐= ☐ ✓ ✗ 6 $$5^6 \div 5 \times 6^9 \div 6^7$$as the product of two powers ☐= ☐ ✓ ✗
Check

This is Power Play level 5. You can also try:
Level 1 Level 2 Level 3 Level 4 Level 6 Level 7

## 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.

## Maths Map

Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.

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

https://www.Transum.org/go/?Num=1074

## Description of Levels

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Level 1 - The basics involving squares, cubes, square roots, cube roots etc.

Level 2 - Writing repeated multiplications as powers

Level 3 - Including division and brackets

Level 4 - The first law of indices with numbers

Level 5 - The second law of indices with numbers

Level 6 - The third law of indices with numbers

Level 7 - The laws of indices with variables

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).

More on this topic 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.

This set of exercises was suggested by Mark Pyle.

## Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

## Help

If you feel as though you'd like to get a better understanding of this topic before working through the levels try the Indices Exercise. Below you can see that video that was made for that exercise.

### 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.

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.

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