Pre-Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Simplify the numerator.

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Step 3.1

Multiply $x$ by $x$ by adding the exponents.

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Step 3.1.1

Move $x$ .

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

Step 3.1.2

Multiply $x$ by $x$ .

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

Step 3.2

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

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Step 3.2.1

Move $y^{3}$ .

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

Step 3.2.2

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

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

Step 3.2.3

Add $3$ and $2$ .

${(\frac{x^{2} y^{5}}{3})}^{4}$

Step 4

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

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Step 4.1

Apply the product rule to $\frac{x^{2} y^{5}}{3}$ .

$\frac{{(x^{2} y^{5})}^{4}}{3^{4}}$

Step 4.2

Apply the product rule to $x^{2} y^{5}$ .

$\frac{{(x^{2})}^{4} {(y^{5})}^{4}}{3^{4}}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply the exponents in ${(x^{2})}^{4}$ .

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Step 5.1.1

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

$\frac{x^{2 \cdot 4} {(y^{5})}^{4}}{3^{4}}$

Step 5.1.2

Multiply $2$ by $4$ .

$\frac{x^{8} {(y^{5})}^{4}}{3^{4}}$

Step 5.2

Multiply the exponents in ${(y^{5})}^{4}$ .

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Step 5.2.1

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

$\frac{x^{8} y^{5 \cdot 4}}{3^{4}}$

Step 5.2.2

Multiply $5$ by $4$ .

$\frac{x^{8} y^{20}}{3^{4}}$

Step 6

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

$\frac{x^{8} y^{20}}{81}$