Write the Fraction in Simplest Form ((4m^4)^2)/(12m^5)

$\frac{{(4 m^{4})}^{2}}{12 m^{5}}$

Step 1

Simplify the numerator.

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

$\frac{4^{2} {(m^{4})}^{2}}{12 m^{5}}$

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

$\frac{16 {(m^{4})}^{2}}{12 m^{5}}$

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

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

$\frac{16 m^{4 \cdot 2}}{12 m^{5}}$

Multiply $4$ by $2$ .

$\frac{16 m^{8}}{12 m^{5}}$

Step 2

Cancel the common factor of $16$ and $12$ .

Factor $4$ out of $16 m^{8}$ .

$\frac{4 (4 m^{8})}{12 m^{5}}$

Cancel the common factors.

Factor $4$ out of $12 m^{5}$ .

$\frac{4 (4 m^{8})}{4 (3 m^{5})}$

Cancel the common factor.

$\frac{4 (4 m^{8})}{4 (3 m^{5})}$

Rewrite the expression.

$\frac{4 m^{8}}{3 m^{5}}$

Step 3

Cancel the common factor of $m^{8}$ and $m^{5}$ .

Factor $m^{5}$ out of $4 m^{8}$ .

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

Cancel the common factors.

Factor $m^{5}$ out of $3 m^{5}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{4 m^{3}}{3}$