Question

State True or False.

$(\frac{27}{64}{)}^{-\frac{2}{3}}$ is equal to $1\frac{8}{9}$.

• A. True
• B. False

Answer 1

The correct option is B False

$\Rightarrow {\left(\frac{27}{64}\right)}^{-\frac{2}{3}}$
$\Rightarrow {\left(\frac{64}{27}\right)}^{\frac{2}{3}}$
$\Rightarrow 27=3^{3}and64=4^3$
$\Rightarrow {\left(\frac{4^3}{3^3}\right)}^{\frac{2}{3}}$
$\Rightarrow \frac{4^{3\cdot \frac{2}{3}}}{3^{3\cdot \frac{2}{3}}}\Rightarrow \frac{4^2}{3^2}$
$\Rightarrow \frac{16}{9}=1\frac{7}{9}$