Fractional and negative indices

3 exam-style questions. Answers and the mark for each step are on the last page.

Question 1Non-calculator · 6 marks
Find the value of each expression. Do not use a calculator.
(a) $25^{\frac{1}{2}}$ (1)
(b) $8^{-1}$ (1)
(c) $27^{\frac{2}{3}}$ (2)
(d) $\left(\frac{4}{9}\right)^{-\frac{1}{2}}$ (2)
Question 2Non-calculator · 5 marks
Work with exact values and no calculator.
(a) Work out $27^{2/3}\times16^{-1/2}$ . (3)
(b) Solve $3^x=1/27$ . (2)
Question 3Non-calculator · 6 marks
Show clear working. Do not use a calculator.
(a) Solve $4^x \times 2^{x + 3} = 32^2$ . You must show your working. (4)
(b) $9^{\frac{1}{2}} \times 27^n = 3^{-4}$ . Find the value of $n$ . You must show your working. (2)

Answers and marks

(a) $5$

(b) $\frac{1}{8}$

(c) $9$

(d) $\frac{3}{2}$

(a) $\frac{9}{4}$

(b) $-3$

(a) $x = \frac{7}{3}$

(b) $n = -\frac{5}{3}$

Fractional and negative indices

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