Simplify ((q^4)^-3)/(q^-15)

$\frac{{(q^{4})}^{- 3}}{q^{- 15}}$

Simplify the expression.

Move ${(q^{4})}^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{q^{- 15} {(q^{4})}^{3}}$

Move $q^{- 15}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{q^{15}}{{(q^{4})}^{3}}$

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

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

$\frac{q^{15}}{q^{4 \cdot 3}}$

Multiply $4$ by $3$ .

$\frac{q^{15}}{q^{12}}$

Cancel the common factor of $q^{15}$ and $q^{12}$ .

Factor $q^{12}$ out of $q^{15}$ .

$\frac{q^{12} q^{3}}{q^{12}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{q^{12} q^{3}}{q^{12} \cdot 1}$

Cancel the common factor.

$\frac{q^{12} q^{3}}{q^{12} \cdot 1}$

Rewrite the expression.

$\frac{q^{3}}{1}$

Divide $q^{3}$ by $1$ .

$q^{3}$