Precalculus Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Move $y^{2}$ .

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

Step 2.2

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

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

Step 2.3

Add $2$ and $3$ .

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

Step 3

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

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Step 3.1

Factor $x$ out of $x^{3}$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $x$ out of $x y^{5}$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

Apply basic rules of exponents.

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Step 4.1

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

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

Step 4.2

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

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Step 4.2.1

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

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

Step 4.2.2

Multiply $2$ by $2$ .

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

Step 4.3

Multiply the exponents in ${(y^{5})}^{2}$ .

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Step 4.3.1

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

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

Step 4.3.2

Multiply $5$ by $2$ .

$\frac{x^{4}}{y^{10}}$