Precalculus Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Apply basic rules of exponents.

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Step 4.1

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

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

Step 4.2

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

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Step 4.2.1

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

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

Step 4.2.2

Multiply $3$ by $2$ .

$\frac{x^{6}}{y^{2}} {(x y^{2})}^{2}$

Step 4.3

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

$\frac{x^{6}}{y^{2}} (x^{2} {(y^{2})}^{2})$

Step 4.4

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

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Step 4.4.1

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

$\frac{x^{6}}{y^{2}} (x^{2} y^{2 \cdot 2})$

Step 4.4.2

Multiply $2$ by $2$ .

$\frac{x^{6}}{y^{2}} (x^{2} y^{4})$

Step 5

Cancel the common factor of $y^{2}$ .

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Step 5.1

Factor $y^{2}$ out of $x^{2} y^{4}$ .

$\frac{x^{6}}{y^{2}} (y^{2} (x^{2} y^{2}))$

Step 5.2

Cancel the common factor.

$\frac{x^{6}}{y^{2}} (y^{2} (x^{2} y^{2}))$

Step 5.3

Rewrite the expression.

$x^{6} (x^{2} y^{2})$

Step 6

Multiply $x^{6}$ by $x^{2}$ by adding the exponents.

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Step 6.1

Move $x^{2}$ .

$x^{2} x^{6} y^{2}$

Step 6.2

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

$x^{2 + 6} y^{2}$

Step 6.3

Add $2$ and $6$ .

$x^{8} y^{2}$