# Exam-Style Questions on Indices

## Problems on Indices adapted from questions set in previous Mathematics exams.

### 1.

GCSE Higher

Without using a calculator, show clearly that $$27^{\frac23}$$ is equal to $$9$$.

### 2.

GCSE Higher
$$9^{\frac{1}{3}} \times 3^n = 27^{\frac{4}{5}}$$

Work out the exact value of $$n$$.

### 3.

GCSE Higher

Without using a calculator find the values of the following:

(a) $$25^{-\frac12}$$

(b) $$\left( \frac{27}{64} \right)^{ \frac23}$$

### 4.

GCSE Higher

(a) The $$n$$th term of a sequence is $$2^n+2^{n+1}$$

Work out the 8th term of the sequence.

(b) The $$n$$th term of a different sequence is $$9(3^n + 3^{n+1})$$

Expand and express this expression as the sum of two powers of three.

### 5.

GCSE Higher

$$y = a \times b^{x – 2}$$ where $$a$$ and $$b$$ are numbers.

$$y = 5$$ when $$x = 2$$

$$y = 0.005$$ when $$x = 5$$

Work out the value of $$y$$ when $$x = 4$$

The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

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