How do you evaluate and simplify 1/(81^-(3/4))?

Mar 22, 2018

$\frac{1}{81} ^ \left(- \frac{3}{4}\right) = 27$

Explanation:

We use identities $\frac{1}{a} ^ \left(- n\right) = {a}^{n}$ and ${\left({a}^{m}\right)}^{n} = {a}^{m \times n}$

hence $\frac{1}{81} ^ \left(- \frac{3}{4}\right)$

= ${81}^{\frac{3}{4}}$

= ${\left({3}^{4}\right)}^{\frac{3}{4}}$

= ${3}^{4 \times \frac{3}{4}}$

= ${3}^{3}$

= $27$