Simplify (3x^-3y^3)/(9x^2(y^-3)^2)

$\frac{3 x^{- 3} y^{3}}{9 x^{2} {(y^{- 3})}^{2}}$

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

$\frac{3 y^{3}}{9 x^{2} {(y^{- 3})}^{2} x^{3}}$

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$\frac{3 y^{3}}{9 (x^{3} x^{2}) {(y^{- 3})}^{2}}$

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

$\frac{3 y^{3}}{9 x^{3 + 2} {(y^{- 3})}^{2}}$

Add $3$ and $2$ .

$\frac{3 y^{3}}{9 x^{5} {(y^{- 3})}^{2}}$

Cancel the common factor of $3$ and $9$ .

Factor $3$ out of $3 y^{3}$ .

$\frac{3 (y^{3})}{9 x^{5} {(y^{- 3})}^{2}}$

Cancel the common factors.

Factor $3$ out of $9 x^{5} {(y^{- 3})}^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the denominator.

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

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

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

Multiply $- 3$ by $2$ .

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

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

$\frac{y^{3}}{3 x^{5} \frac{1}{y^{6}}}$

Combine exponents.

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

$\frac{y^{3}}{x^{5} \frac{3}{y^{6}}}$

Combine $x^{5}$ and $\frac{3}{y^{6}}$ .

$\frac{y^{3}}{\frac{x^{5} \cdot 3}{y^{6}}}$

Move $3$ to the left of $x^{5}$ .

$\frac{y^{3}}{\frac{3 x^{5}}{y^{6}}}$

Multiply the numerator by the reciprocal of the denominator.

$y^{3} \frac{y^{6}}{3 x^{5}}$

Multiply $y^{3} \frac{y^{6}}{3 x^{5}}$ .

Combine $y^{3}$ and $\frac{y^{6}}{3 x^{5}}$ .

$\frac{y^{3} y^{6}}{3 x^{5}}$

Multiply $y^{3}$ by $y^{6}$ by adding the exponents.

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

$\frac{y^{3 + 6}}{3 x^{5}}$

Add $3$ and $6$ .

$\frac{y^{9}}{3 x^{5}}$