Simplify (3(q^5)^4)/(5q^4)

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

Step 1

Multiply the exponents in ${(q^{5})}^{4}$ .

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

$\frac{3 q^{5 \cdot 4}}{5 q^{4}}$

Multiply $5$ by $4$ .

$\frac{3 q^{20}}{5 q^{4}}$

Step 2

Cancel the common factor of $q^{20}$ and $q^{4}$ .

Factor $q^{4}$ out of $3 q^{20}$ .

$\frac{q^{4} (3 q^{16})}{5 q^{4}}$

Cancel the common factors.

Factor $q^{4}$ out of $5 q^{4}$ .

$\frac{q^{4} (3 q^{16})}{q^{4} \cdot 5}$

Cancel the common factor.

$\frac{q^{4} (3 q^{16})}{q^{4} \cdot 5}$

Rewrite the expression.

$\frac{3 q^{16}}{5}$