# How do you simplify (81/16*p^8/q^-3)^(-3/4)?

Nov 8, 2016

$\implies {\left(\frac{81 {p}^{8}}{16 {q}^{- 3}}\right)}^{- \frac{3}{4}}$

$\implies {\left(\frac{16 {q}^{- 3}}{81 {p}^{8}}\right)}^{\frac{3}{4}}$

$\implies {\left(\frac{16}{81 {p}^{8} {q}^{3}}\right)}^{\frac{3}{4}}$

$\implies {\left(\sqrt[4]{\frac{16}{81 {p}^{8} {q}^{3}}}\right)}^{3}$

$\implies {\left(\frac{2}{3 {p}^{2}} \sqrt[4]{\frac{1}{q} ^ 3}\right)}^{3}$

$\implies \frac{8}{27 {p}^{6}} \times \frac{1}{q} ^ \left(\frac{9}{4}\right)$

$\implies \frac{8}{27 {p}^{6} {q}^{\frac{9}{4}}}$

Hopefully this helps!