Question

Compute $\dfrac{(2/3)^3}{(2/9)^2}$.

Answer 1

$\bf \cfrac{\left( \frac{2}{3} \right)^3}{\left( \frac{2}{9} \right)^2}\implies \cfrac{\quad \frac{2^3}{3^3}\quad }{\frac{2^2}{9^2}}\implies \cfrac{2^3}{3^3}\cdot \cfrac{9^2}{2^2}\implies \cfrac{2^3}{3^3}\cdot \cfrac{(3^2)^2}{2^2}\implies \cfrac{2^3}{3^3}\cdot \cfrac{3^4}{2^2} \\\\\\ \cfrac{2^3}{2^2}\cdot \cfrac{3^4}{3^3}\implies 2^3\cdot 2^{-2}\cdot 3^4\cdot 3^{-3}\implies 2^{3-2}\cdot 3^{4-3}\implies 2^1\cdot 3^1\implies 6$