Pre-Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Simplify the denominator.

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Step 3.1

Multiply $x^{- 1}$ by $x^{2}$ by adding the exponents.

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Step 3.1.1

Move $x^{2}$ .

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

Step 3.1.2

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

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

Step 3.1.3

Subtract $1$ from $2$ .

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

Step 3.2

Simplify $2^{- 2} x^{1} y^{- 2}$ .

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

Step 3.3

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

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Step 3.3.1

Move $y^{3}$ .

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

Step 3.3.2

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

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

Step 3.3.3

Subtract $2$ from $3$ .

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

Step 3.4

Simplify $2^{- 2} x y^{1}$ .

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

Step 4

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

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

Step 5

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

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

Step 6

Change the sign of the exponent by rewriting the base as its reciprocal.

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

Step 7

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

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Step 7.1

Apply the product rule to $\frac{x y}{4}$ .

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

Step 7.2

Apply the product rule to $x y$ .

$\frac{x^{3} y^{3}}{4^{3}}$

Step 8

Raise $4$ to the power of $3$ .

$\frac{x^{3} y^{3}}{64}$