Dr Tim's Indices Challenge

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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Questions written by Dr Tim Honeywill (@HoneywillTim)

Background photograph by Yvonne Brown

Reminders

$$5^1=5$$ $$5^0=1$$ $$5^{-1}=\frac15$$

$$5^a \times 5^b = 5^{a+b}$$ $$5^a \div 5^b = 5^{a-b}$$ $$(5^a)^b = 5^{ab}$$

The answers, particularly at level 2, can be written a variety of different forms even within the 'alphabetical order' constraint. If you get an answer marked wrong but are convinced it is correct try writing it in a different format.

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.

1. If \(2^n=2^p \times 2^q\), write down an expression for \(n\) in terms of \(p\) and \(q\).	n=
2. If \(2^n= 2^p \times 2^q \times 2\), write down an expression for \(n\) in terms of \(p\) and \(q\).	n=
3. If \(2^n= 2^p \times 2^q \times 8\), write down an expression for \(n\) in terms of \(p\) and \(q\).	n=
4. If \(2^n= \frac {2^p \times 2^q}{2} \), write down an expression for \(n\) in terms of \(p\) and \(q\).	n=
5. If \(2^n=4^p \times 8^q \times 16\), write down an expression for \(n\) in terms of \(p\) and \(q\).	n=
6. If \(2^n= \frac{2 \times 4^p}{4 \times 2^q}\), write down an expression for \(n\) in terms of \(p\) and \(q\).	n=
7. If \(2^n=4^p \times 8^n\), write down an expression for \(n\) in terms of \(p\).	n=
8. If \(2^n=(2 \times 4^p )^2 \times (8 \times 16^q )^3\), write down an expression for \(n\) in terms of \(p\) and \(q\).	n=
9. If \(3^n=9^p \times 27\), write down an expression for \(n\) in terms of \(p\).	n=
10. If \(3 \times 3^n= 9 \times 9^p \times 27 \times 27^q\), write down an expression for \(n\) in terms of \(p\) and \(q\).	n=

Dr Tim's Indices Challenge

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

Indices Level 1 Level 2 Exam-Style Description Help More Indices

Instructions

More Activities:

Featured Activity

Numskull

Answers

Go Maths

Maths Map

Teachers

Description of Levels

Curriculum Reference

Reminders

Typing Mathematical Notation