Evaluate ((-2m^4)^2)/(8m^2)

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

Step 1

Simplify the numerator.

Apply the product rule to $- 2 m^{4}$ .

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

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

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

Multiply the exponents in ${(m^{4})}^{2}$ .

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

$\frac{4 m^{4 \cdot 2}}{8 m^{2}}$

Multiply $4$ by $2$ .

$\frac{4 m^{8}}{8 m^{2}}$

Step 2

Reduce the expression by cancelling the common factors.

Cancel the common factor of $4$ and $8$ .

Factor $4$ out of $4 m^{8}$ .

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

Cancel the common factors.

Factor $4$ out of $8 m^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{m^{8}}{2 m^{2}}$

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

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

$\frac{m^{2} m^{6}}{2 m^{2}}$

Cancel the common factors.

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

$\frac{m^{2} m^{6}}{m^{2} \cdot 2}$

Cancel the common factor.

$\frac{m^{2} m^{6}}{m^{2} \cdot 2}$

Rewrite the expression.

$\frac{m^{6}}{2}$