Quick questions on Indices and laws of exponents explained: O-Level A-Maths

5short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What are solving simple exponential equations?

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If you can write both sides of an equation to the same base, then equal powers force equal indices:

a^x = a^y \Rightarrow x = y

. This turns an index equation into an ordinary algebraic one.

What is common bases to recognise?

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It helps to know the small powers of the usual bases:

4 = 2^2

8 = 2^3

16 = 2^4

9 = 3^2

27 = 3^3

25 = 5^2

. Spotting these lets you rewrite both sides of an equation such as

8^x = 4

to a common base

2

and equate indices at once.

What is q1?

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Simplify

a^5 \times a^{-2} \div a^{0}

. [2 marks]

What is q2?

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Evaluate

27^{2/3}

. [2 marks]

What is q3?

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Solve

4^{x} = 8

. [2 marks]

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