Question 176

By what number should $(- 8)^{- 3}$ be multiplied so that the product may be equal to $(- 6)^{- 3}$ ?

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Solution

Let x be the number multiplied with $(- 8)^{- 3}$ to get the product equal to $(- 6)^{- 3}$ .
$\Rightarrow x \times (- 8)^{- 3} = (- 6)^{- 3} \Rightarrow x = \frac{(- 6)^{- 3}}{(- 8)^{- 3}} = \frac{(- 8)^{3}}{(- 6)^{3}} = \frac{(8)^{3}}{(6)^{3}} = \frac{(2 \times 4)^{3}}{(2 \times 3)^{3}} = \frac{2^{3} \times 4^{3}}{2^{3} \times 3^{3}} = \frac{4^{3}}{3^{3}} = (\frac{4}{3})^{3}$

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