Simplify ((2x^-1y)/(x^-3y^-2))^-3

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

Step 1

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

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

Step 2

Move $y^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 3

Multiply $x^{- 1}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

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

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

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

Subtract $1$ from $3$ .

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

Step 4

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

Move $y^{2}$ .

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

Multiply $y^{2}$ by $y$ .

Raise $y$ to the power of $1$ .

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

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

${(2 x^{2} y^{2 + 1})}^{- 3}$

Add $2$ and $1$ .

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

Step 5

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

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

Step 6

Simplify the denominator.

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

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

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

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

Raise $2$ to the power of $3$ .

$\frac{1}{8 {(x^{2})}^{3} {(y^{3})}^{3}}$

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

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

$\frac{1}{8 x^{2 \cdot 3} {(y^{3})}^{3}}$

Multiply $2$ by $3$ .

$\frac{1}{8 x^{6} {(y^{3})}^{3}}$

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

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

$\frac{1}{8 x^{6} y^{3 \cdot 3}}$

Multiply $3$ by $3$ .

$\frac{1}{8 x^{6} y^{9}}$

Simplify ((2x^-1y)/(x^-3y^-2))^-3

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