Express $27 / 64$ and $- 27 / 64$ as powers of a rational number.

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Solution

$∵ 27 = 3 \times 3 \times 3 = 3^{3}$
$\Rightarrow - 27 = - 3 \times - 3 \times - 3 = (- 3)^{3}$
$\Rightarrow 64 = 4 \times 4 \times 4 = 4^{3}$
Now use, ${(\frac{a}{b})}^{m} = \frac{a^{m}}{b^{m}}$
$∴ \frac{27}{64} = \frac{3^{3}}{4^{3}} = {(\frac{3}{4})}^{3}$
$∴ \frac{- 27}{64} = \frac{(- 3)^{3}}{4^{3}} = {(\frac{- 3}{4})}^{3}$

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Question 94

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Express $\frac{27}{64}$ and $\frac{- 27}{64}$ as powers of a rational number.

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$(i) \frac{27}{64} (i i) \frac{125}{128} (i i i) 0.001331 (i v) 0.04$

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