Evaluate ((q^6)^-2)/(q^-16)

$\frac{{(q^{6})}^{- 2}}{q^{- 16}}$

Simplify the expression.

Move ${(q^{6})}^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{q^{- 16} {(q^{6})}^{2}}$

Move $q^{- 16}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{q^{16}}{{(q^{6})}^{2}}$

Multiply the exponents in ${(q^{6})}^{2}$ .

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

$\frac{q^{16}}{q^{6 \cdot 2}}$

Multiply $6$ by $2$ .

$\frac{q^{16}}{q^{12}}$

Cancel the common factor of $q^{16}$ and $q^{12}$ .

Factor $q^{12}$ out of $q^{16}$ .

$\frac{q^{12} q^{4}}{q^{12}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{q^{12} q^{4}}{q^{12} \cdot 1}$

Cancel the common factor.

$\frac{q^{12} q^{4}}{q^{12} \cdot 1}$

Rewrite the expression.

$\frac{q^{4}}{1}$

Divide $q^{4}$ by $1$ .

$q^{4}$