Simplify (3x^-3y)^3*2xy^-4

${(3 x^{- 3} y)}^{3} \cdot 2 x y^{- 4}$

Rewrite using the commutative property of multiplication.

$2 {(3 x^{- 3} y)}^{3} x y^{- 4}$

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

$2 {(3 \frac{1}{x^{3}} y)}^{3} x y^{- 4}$

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

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

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

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

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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

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

Apply the product rule to $3 y$ .

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

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

$2 \frac{27 y^{3}}{{(x^{3})}^{3}} x y^{- 4}$

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

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

$2 \frac{27 y^{3}}{x^{3 \cdot 3}} x y^{- 4}$

Multiply $3$ by $3$ .

$2 \frac{27 y^{3}}{x^{9}} x y^{- 4}$

Multiply $2 \frac{27 y^{3}}{x^{9}}$ .

Combine $2$ and $\frac{27 y^{3}}{x^{9}}$ .

$\frac{2 (27 y^{3})}{x^{9}} x y^{- 4}$

Multiply $27$ by $2$ .

$\frac{54 y^{3}}{x^{9}} x y^{- 4}$

Cancel the common factor of $x$ .

Factor $x$ out of $x^{9}$ .

$\frac{54 y^{3}}{x \cdot x^{8}} x y^{- 4}$

Cancel the common factor.

$\frac{54 y^{3}}{x \cdot x^{8}} x y^{- 4}$

Rewrite the expression.

$\frac{54 y^{3}}{x^{8}} y^{- 4}$

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

$\frac{54 y^{3}}{x^{8}} \cdot \frac{1}{y^{4}}$

Combine.

$\frac{54 y^{3} \cdot 1}{x^{8} y^{4}}$

Cancel the common factor of $y^{3}$ and $y^{4}$ .

Factor $y^{3}$ out of $54 y^{3} \cdot 1$ .

$\frac{y^{3} (54 \cdot 1)}{x^{8} y^{4}}$

Cancel the common factors.

Factor $y^{3}$ out of $x^{8} y^{4}$ .

$\frac{y^{3} (54 \cdot 1)}{y^{3} (x^{8} y)}$

Cancel the common factor.

$\frac{y^{3} (54 \cdot 1)}{y^{3} (x^{8} y)}$

Rewrite the expression.

$\frac{54 \cdot 1}{x^{8} y}$

Multiply $54$ by $1$ .

$\frac{54}{x^{8} y}$

Simplify (3x^-3y)^3*2xy^-4

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