Question

By what number should we multiply $3^{\frac{-3}{4}}$ so that the product is equal to $9^{\frac{3}{8}}$

Answer 1

Let $x$ be the number

$x\times 3^{\frac{-3}{4}}=9^{3/8}$

$\Rightarrow x=3^{3/4}\times 9^{3/8}$

$=3^{3/4}\times (3^2{)}^{3/8}$

$=3^{3/4}\times 3^{2\times \frac{3}{8}}$

$=3^{3/4}\times 3^{3/4}$

$=3^{3/4+3/4}$

$=3^{6/4}$

$=3^{3/2}$

$=(3^{1/2}{)}^3$

$=(\sqrt{3}{)}^3$

$=3\sqrt{3}$

$\therefore x=3\sqrt{3}$