Question

State True or False.

$(27{)}^{\frac{2}{3}}÷(\frac{81}{16}{)}^{-\frac{1}{4}}$ is equal to $13\frac{1}{2}$.

• A. True
• B. False

Answer 1

The correct option is A True

$\Rightarrow (27{)}^{\frac{2}{3}}÷(\frac{81}{16}{)}^{-\frac{1}{4}}$
$\Rightarrow (27{)}^{\frac{2}{3}}÷(\frac{16}{81}{)}^{\frac{1}{4}}$
$\Rightarrow 3^{3\cdot \frac{2}{3}}÷\frac{2^{4\cdot \frac{1}{4}}}{3^{4\cdot \frac{1}{4}}}$
$\Rightarrow 3^2÷\frac{2}{3}\Rightarrow 9\times \frac{3}{2}$
$\Rightarrow \frac{27}{2}\Rightarrow 13\frac{1}{2}$