# How do you rewrite ((m^-3n^5)/(mn^-2))^2 using a positive exponent?

Oct 19, 2015

${n}^{14} / {m}^{8}$ is the simplified version of the expression with all positive exponents.

#### Explanation:

Begin by moving all of the exponents to the numerator.

${\left(\frac{{m}^{-} 3 {n}^{5}}{m {n}^{-} 2}\right)}^{2}$

the expression becomes,
${\left({m}^{-} 3 {m}^{-} 1 {n}^{5} {n}^{2}\right)}^{2}$
the exponents change sign when they are brought from the
denominator to the numerator

Combine the exponents for the similar variables
${\left({m}^{- 3 - 1} {n}^{5 + 2}\right)}^{2}$

${\left({m}^{-} 4 {n}^{7}\right)}^{2}$
Now distribute the exponent outside the parenthesis to the
exponents inside by multiplication.
${m}^{-} 8 {n}^{14}$

Now move the variable with the negative exponent to the denominator to make the exponent positive.
${n}^{14} / {m}^{8}$