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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

This is level 2: Dr Tim's tortuous tasks. You can earn a trophy if you get at least 7 questions correct and you do this activity online.

The letters (variables) in your answers should be in alphabetical order with the constant term (if any) at the end.

Use the forward slash / to type a fraction. Press the right arrow key to end the fraction.

1. If \(8^n=2^p \times 2^q\), write down an expression for \(n\) in terms of \(p\) and \(q\).	n=
2. If \(2^n= \sqrt{2^p \times 2^q}\), write down an expression for \(n\) in terms of \(p\) and \(q\).	n=
3. If \( \sqrt{3}= \frac{3^n \times 9^p}{27^q}\) , write down an expression for \(n\) in terms of \(p\) and \(q\).	n=
4. If \( \frac{9^n \times 3^p}{\sqrt{3}}\)=27, write down an expression for \(n\) in terms of \(p\).	n=
5. If \(5\sqrt{5}=(25^p)^2 \div 5^n\), write down an expression for \(n\) in terms of \(p\).	n=
6. If \(7^{3n}=49 \times 7^{2p} \div 7^{3q} \), write down an expression for \(n\) in terms of \(p\) and \(q\).	n=
7. If \(7^{\frac13} \times 7^n=(\frac{7^p}{49^q})^{-1}\), write down an expression for \(n\) in terms of \(p\) and \(q\).	n=
8. If \(4^n=\frac{2^p}{8^q} \times \frac{4^q}{2^n} \), write down an expression for \(n\) in terms of \(p\) and \(q\).	n=
9. If \(6×2^n=4^p-2 \times 2^n\), write down an expression for \(n\) in terms of \(p\) .	n=
10. If \(3×3^n=27^p-6 \times 3^n\), write down an expression for \(n\) in terms of \(p\) .	n=

This is Dr Tim's Indices Challenge level 2. You can also try:
Level 1

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

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Description of Levels

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Indices - The traditional, easier indices questions.

Level 1 - Dr Tim's tricky tasks

Level 2 - Dr Tim's tortuous tasks

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.

Curriculum Reference

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

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.

MathQuill Animation

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