Simplify (4m^2)/((5m^4)^3)

$\frac{4 m^{2}}{{(5 m^{4})}^{3}}$

Step 1

Simplify the denominator.

Apply the product rule to $5 m^{4}$ .

$\frac{4 m^{2}}{5^{3} {(m^{4})}^{3}}$

Raise $5$ to the power of $3$ .

$\frac{4 m^{2}}{125 {(m^{4})}^{3}}$

Multiply the exponents in ${(m^{4})}^{3}$ .

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

$\frac{4 m^{2}}{125 m^{4 \cdot 3}}$

Multiply $4$ by $3$ .

$\frac{4 m^{2}}{125 m^{12}}$

Step 2

Cancel the common factor of $m^{2}$ and $m^{12}$ .

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

$\frac{m^{2} \cdot 4}{125 m^{12}}$

Cancel the common factors.

Factor $m^{2}$ out of $125 m^{12}$ .

$\frac{m^{2} \cdot 4}{m^{2} (125 m^{10})}$

Cancel the common factor.

$\frac{m^{2} \cdot 4}{m^{2} (125 m^{10})}$

Rewrite the expression.

$\frac{4}{125 m^{10}}$