Simplify -(2q^2)/(3(q^-4)^2)

$- \frac{2 q^{2}}{3 {(q^{- 4})}^{2}}$

Simplify the denominator.

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

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

$- \frac{2 q^{2}}{3 q^{- 4 \cdot 2}}$

Multiply $- 4$ by $2$ .

$- \frac{2 q^{2}}{3 q^{- 8}}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$- \frac{2 q^{2}}{3 \frac{1}{q^{8}}}$

Combine $3$ and $\frac{1}{q^{8}}$ .

$- \frac{2 q^{2}}{\frac{3}{q^{8}}}$

Multiply the numerator by the reciprocal of the denominator.

$- (2 q^{2} \frac{q^{8}}{3})$

Multiply $2 q^{2} \frac{q^{8}}{3}$ .

Combine $2$ and $\frac{q^{8}}{3}$ .

$- (q^{2} \frac{2 q^{8}}{3})$

Combine $q^{2}$ and $\frac{2 q^{8}}{3}$ .

$- \frac{q^{2} (2 q^{8})}{3}$

Multiply $q^{2}$ by $q^{8}$ by adding the exponents.

Move $q^{8}$ .

$- \frac{q^{8} q^{2} \cdot 2}{3}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- \frac{q^{8 + 2} \cdot 2}{3}$

Add $8$ and $2$ .

$- \frac{q^{10} \cdot 2}{3}$

Move $2$ to the left of $q^{10}$ .

$- \frac{2 q^{10}}{3}$