Simplify (-4(y)^-2)/(3z^-5y^-7)

$\frac{- 4 {(y)}^{- 2}}{3 z^{- 5} y^{- 7}}$

Move $y^{- 7}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{- 4 {(y)}^{- 2} y^{7}}{3 z^{- 5}}$

Move $z^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{- 4 {(y)}^{- 2} y^{7} z^{5}}{3}$

Multiply ${(y)}^{- 2}$ by $y^{7}$ by adding the exponents.

Move $y^{7}$ .

$\frac{- 4 (y^{7} {(y)}^{- 2}) z^{5}}{3}$

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

$\frac{- 4 y^{7 - 2} z^{5}}{3}$

Subtract $2$ from $7$ .

$\frac{- 4 y^{5} z^{5}}{3}$

Move the negative in front of the fraction.

$- \frac{4 y^{5} z^{5}}{3}$