Simplify (m^8n^-4)^(1/4)

${(m^{8} n^{- 4})}^{\frac{1}{4}}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(m^{8} \frac{1}{n^{4}})}^{\frac{1}{4}}$

Step 2

Combine fractions.

Combine $m^{8}$ and $\frac{1}{n^{4}}$ .

${(\frac{m^{8}}{n^{4}})}^{\frac{1}{4}}$

Apply basic rules of exponents.

Apply the product rule to $\frac{m^{8}}{n^{4}}$ .

$\frac{{(m^{8})}^{\frac{1}{4}}}{{(n^{4})}^{\frac{1}{4}}}$

Multiply the exponents in ${(m^{8})}^{\frac{1}{4}}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{m^{8 (\frac{1}{4})}}{{(n^{4})}^{\frac{1}{4}}}$

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$\frac{m^{4 (2) \frac{1}{4}}}{{(n^{4})}^{\frac{1}{4}}}$

Cancel the common factor.

$\frac{m^{4 \cdot 2 \frac{1}{4}}}{{(n^{4})}^{\frac{1}{4}}}$

Rewrite the expression.

$\frac{m^{2}}{{(n^{4})}^{\frac{1}{4}}}$

Step 3

Simplify the denominator.

Multiply the exponents in ${(n^{4})}^{\frac{1}{4}}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{m^{2}}{n^{4 (\frac{1}{4})}}$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{m^{2}}{n^{4 (\frac{1}{4})}}$

Rewrite the expression.

$\frac{m^{2}}{n^{1}}$

Simplify.

$\frac{m^{2}}{n}$