Simplify ((-5m)^4)/((-25m^2)^2)

$\frac{{(- 5 m)}^{4}}{{(- 25 m^{2})}^{2}}$

Step 1

Simplify the numerator.

Apply the product rule to $- 5 m$ .

$\frac{{(- 5)}^{4} m^{4}}{{(- 25 m^{2})}^{2}}$

Raise $- 5$ to the power of $4$ .

$\frac{625 m^{4}}{{(- 25 m^{2})}^{2}}$

Step 2

Simplify the denominator.

Apply the product rule to $- 25 m^{2}$ .

$\frac{625 m^{4}}{{(- 25)}^{2} {(m^{2})}^{2}}$

Raise $- 25$ to the power of $2$ .

$\frac{625 m^{4}}{625 {(m^{2})}^{2}}$

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

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

$\frac{625 m^{4}}{625 m^{2 \cdot 2}}$

Multiply $2$ by $2$ .

$\frac{625 m^{4}}{625 m^{4}}$

Step 3

Reduce the expression by cancelling the common factors.

Cancel the common factor of $625$ .

Cancel the common factor.

$\frac{625 m^{4}}{625 m^{4}}$

Rewrite the expression.

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

Cancel the common factor of $m^{4}$ .

Cancel the common factor.

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

Rewrite the expression.

$1$