Question

Question 176

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

Answer 1

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