Simplify ((2m^8)/(m^2n^4))^4

${(\frac{2 m^{8}}{m^{2} n^{4}})}^{4}$

Step 1

Cancel the common factor of $m^{8}$ and $m^{2}$ .

Factor $m^{2}$ out of $2 m^{8}$ .

${(\frac{m^{2} (2 m^{6})}{m^{2} n^{4}})}^{4}$

Cancel the common factors.

Factor $m^{2}$ out of $m^{2} n^{4}$ .

${(\frac{m^{2} (2 m^{6})}{m^{2} (n^{4})})}^{4}$

Cancel the common factor.

${(\frac{m^{2} (2 m^{6})}{m^{2} n^{4}})}^{4}$

Rewrite the expression.

${(\frac{2 m^{6}}{n^{4}})}^{4}$

Step 2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{2 m^{6}}{n^{4}}$ .

$\frac{{(2 m^{6})}^{4}}{{(n^{4})}^{4}}$

Apply the product rule to $2 m^{6}$ .

$\frac{2^{4} {(m^{6})}^{4}}{{(n^{4})}^{4}}$

Step 3

Simplify the numerator.

Raise $2$ to the power of $4$ .

$\frac{16 {(m^{6})}^{4}}{{(n^{4})}^{4}}$

Multiply the exponents in ${(m^{6})}^{4}$ .

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

$\frac{16 m^{6 \cdot 4}}{{(n^{4})}^{4}}$

Multiply $6$ by $4$ .

$\frac{16 m^{24}}{{(n^{4})}^{4}}$

Step 4

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

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

$\frac{16 m^{24}}{n^{4 \cdot 4}}$

Multiply $4$ by $4$ .

$\frac{16 m^{24}}{n^{16}}$