Question

State True or False.

Simplify: $(\frac{256a^{16}}{81b^4}{)}^{-\frac{3}{4}}$, then answer is $\frac{27b^3}{64a^{12}}=\frac{27}{64}{a}^{-12}{b}^3$.

• A. True
• B. False

Answer 1

The correct option is A True

As given $(\frac{256a^{16}}{81b^4}{)}^{-\frac{3}{4}}$
$\Rightarrow {\left(\frac{4^4{a}^{16}}{3^4{b}^4}\right)}^{-\frac{3}{4}}$
$\Rightarrow \frac{\left(4^{4\cdot -\frac{3}{4}}{a}^{16\cdot -\frac{3}{4}}\right)}{\left(3^{4\cdot -\frac{3}{4}}{b}^{4\cdot -\frac{3}{4}}\right)}$
$\Rightarrow \left(\frac{4^{-3}{a}^{-12}}{3^{-3}{b}^{-3}}\right)$
$\Rightarrow \frac{27b^3}{64a^{12}}$
$\Rightarrow \frac{27}{64}{a}^{-12}{b}^3$