Simplify (-3(y^-2)^3)/(5y^2)

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

Simplify the numerator.

Multiply the exponents in ${(y^{- 2})}^{3}$ .

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

$\frac{- 3 y^{- 2 \cdot 3}}{5 y^{2}}$

Multiply $- 2$ by $3$ .

$\frac{- 3 y^{- 6}}{5 y^{2}}$

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

$\frac{- 3 \frac{1}{y^{6}}}{5 y^{2}}$

Combine fractions.

Combine $- 3$ and $\frac{1}{y^{6}}$ .

$\frac{\frac{- 3}{y^{6}}}{5 y^{2}}$

Move the negative in front of the fraction.

$\frac{- \frac{3}{y^{6}}}{5 y^{2}}$

Multiply the numerator by the reciprocal of the denominator.

$- \frac{3}{y^{6}} \cdot \frac{1}{5 y^{2}}$

Multiply $- \frac{3}{y^{6}} \cdot \frac{1}{5 y^{2}}$ .

Multiply $\frac{1}{5 y^{2}}$ by $\frac{3}{y^{6}}$ .

$- \frac{3}{5 y^{2} y^{6}}$

Multiply $y^{2}$ by $y^{6}$ by adding the exponents.

Move $y^{6}$ .

$- \frac{3}{5 (y^{6} y^{2})}$

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

$- \frac{3}{5 y^{6 + 2}}$

Add $6$ and $2$ .

$- \frac{3}{5 y^{8}}$