Simplify ((3x^-2y)^3)/(9x^5)

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

Simplify the numerator.

Apply the product rule to $3 x^{- 2} y$ .

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

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

$\frac{{(3 \frac{1}{x^{2}})}^{3} y^{3}}{9 x^{5}}$

Combine $3$ and $\frac{1}{x^{2}}$ .

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

Apply the product rule to $\frac{3}{x^{2}}$ .

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

Raise $3$ to the power of $3$ .

$\frac{\frac{27}{{(x^{2})}^{3}} y^{3}}{9 x^{5}}$

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

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

$\frac{\frac{27}{x^{2 \cdot 3}} y^{3}}{9 x^{5}}$

Multiply $2$ by $3$ .

$\frac{\frac{27}{x^{6}} y^{3}}{9 x^{5}}$

Combine $\frac{27}{x^{6}}$ and $y^{3}$ .

$\frac{\frac{27 y^{3}}{x^{6}}}{9 x^{5}}$

Multiply the numerator by the reciprocal of the denominator.

$\frac{27 y^{3}}{x^{6}} \cdot \frac{1}{9 x^{5}}$

Combine.

$\frac{27 y^{3} \cdot 1}{x^{6} (9 x^{5})}$

Multiply $x^{6}$ by $x^{5}$ by adding the exponents.

Move $x^{5}$ .

$\frac{27 y^{3} \cdot 1}{x^{5} x^{6} \cdot 9}$

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

$\frac{27 y^{3} \cdot 1}{x^{5 + 6} \cdot 9}$

Add $5$ and $6$ .

$\frac{27 y^{3} \cdot 1}{x^{11} \cdot 9}$

Multiply $27 y^{3}$ by $1$ .

$\frac{27 y^{3}}{x^{11} \cdot 9}$

Cancel the common factor of $27$ and $9$ .

Factor $9$ out of $27 y^{3}$ .

$\frac{9 (3 y^{3})}{x^{11} \cdot 9}$

Cancel the common factors.

Factor $9$ out of $x^{11} \cdot 9$ .

$\frac{9 (3 y^{3})}{9 \cdot x^{11}}$

Cancel the common factor.

$\frac{9 (3 y^{3})}{9 \cdot x^{11}}$

Rewrite the expression.

$\frac{3 y^{3}}{x^{11}}$