How do you simplify (m^4/(5n^9))^3 and write it using only positive exponents?

Apr 23, 2017

$= {m}^{12} / \left(125 {n}^{27}\right)$

Explanation:

The power law of indices: raising a power to a power, multiply the indices.

${\left({x}^{m}\right)}^{n} = {x}^{m \times n} = {x}^{m n}$

${\left({m}^{4} / \left(5 {n}^{9}\right)\right)}^{3}$

= m^(4xx3)/(5^3n^(9xx3)

$= {m}^{12} / \left(125 {n}^{27}\right)$

There are only positive indices.