# How do you simplify ((2s^-1t^3)/(6s^2t^-4))^-3?

Sep 5, 2016

Start by getting rid of the exponent on the outside.

$= {\left(\frac{6 {s}^{2} {t}^{-} 4}{2 {s}^{-} 1 {t}^{3}}\right)}^{3}$

Use the quotient rule $\left({a}^{n} / {a}^{m} = {a}^{n - m}\right)$ and division to simplify further.

$= {\left(3 {s}^{3} {t}^{-} 7\right)}^{3}$

Use the power rule ${\left({a}^{n}\right)}^{m} = {a}^{n \times m}$ to simplify.

$= 27 {s}^{9} {t}^{-} 21$

$= \frac{27 {s}^{9}}{{t}^{21}}$

Hopefully this helps!