Question

Simplify
(8)^-2/3 ÷ (16)^-3/4

Answer 1

${(8)}^{ \frac{ - 2}{3} } \div {(16)}^{ \frac{ - 3}{4} } \\ \\ = {\bigg( \frac{1}{8} \bigg)}^{ \frac{2}{3} } \div {\bigg( \frac{1}{16} \bigg)}^{ \frac{3}{4} } \\ \\ = {\bigg( \frac{1}{ {8}^{ \frac{1}{3} } } \bigg)}^{2} \div {\bigg( \frac{1}{ {16}^{ \frac{1}{4} } } \bigg)}^{ 3 } \\ \\ = {\bigg( \frac{1}{2} \bigg)}^{2 } \div {\bigg( \frac{1}{2} \bigg)}^{ 3 } \\ \\ = \frac{1}{4} \div \frac{1}{8} \\ \\ = \frac{1}{4} \times \frac{8}{1} \\ \\ = 2$

Answer 2

Answer:

→ $\Huge\boxed{2}$

Step-by-step explanation:

$\begin{lgathered}{(8)}^{ \frac{ - 2}{3} } \div {(16)}^{ \frac{ - 3}{4} } \\ \\ = {\bigg( \frac{1}{8} \bigg)}^{ \frac{2}{3} } \div {\bigg( \frac{1}{16} \bigg)}^{ \frac{3}{4} } \\ \\ = {\bigg( \frac{1}{ {8}^{ \frac{1}{3} } } \bigg)}^{2} \div {\bigg( \frac{1}{ {16}^{ \frac{1}{4} } } \bigg)}^{ 3 } \\ \\ = {\bigg( \frac{1}{2} \bigg)}^{2 } \div {\bigg( \frac{1}{2} \bigg)}^{ 3 } \\ \\ = \frac{1}{4} \div \frac{1}{8} \\ \\ = \frac{1}{4} \times \frac{8}{1} \\ \\ = 2\end{lgathered}$