How do you simplify the expression  27^(-2/3)?

Jun 21, 2016

${27}^{- \frac{2}{3}} = \frac{1}{9}$

Explanation:

${27}^{- \frac{2}{3}}$

= ${\left({3}^{3}\right)}^{- \frac{2}{3}}$ and as ${\left({a}^{m}\right)}^{n} = {a}^{m \times n}$

The above is equal to ${3}^{3 \times - \frac{2}{3}}$

= ${3}^{- 2}$

As ${a}^{- m} = \frac{1}{a} ^ m$

${3}^{- 2} = \frac{1}{3} ^ 2 = \frac{1}{9}$