Algebra Examples

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

Step 1

Combine.

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

Step 2

Simplify.

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Step 2.1

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

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

Step 2.2

Move $y^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 3

Multiply $y$ by $y^{4}$ by adding the exponents.

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Step 3.1

Move $y^{4}$ .

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

Step 3.2

Multiply $y^{4}$ by $y$ .

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Step 3.2.1

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

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

Step 3.2.2

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

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

Step 3.3

Add $4$ and $1$ .

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

Step 4

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

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Step 4.1

Factor $x$ out of $x^{3} y^{5}$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $x$ out of $x {(y^{- 3})}^{2} {(x^{2})}^{2}$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

Simplify the denominator.

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Step 5.1

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

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Step 5.1.1

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

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

Step 5.1.2

Multiply $- 3$ by $2$ .

$\frac{x^{2} y^{5}}{y^{- 6} {(x^{2})}^{2}}$

Step 5.2

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

$\frac{x^{2} y^{5}}{\frac{1}{y^{6}} {(x^{2})}^{2}}$

Step 5.3

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

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Step 5.3.1

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

$\frac{x^{2} y^{5}}{\frac{1}{y^{6}} x^{2 \cdot 2}}$

Step 5.3.2

Multiply $2$ by $2$ .

$\frac{x^{2} y^{5}}{\frac{1}{y^{6}} x^{4}}$

Step 6

Combine $\frac{1}{y^{6}}$ and $x^{4}$ .

$\frac{x^{2} y^{5}}{\frac{x^{4}}{y^{6}}}$

Step 7

Multiply the numerator by the reciprocal of the denominator.

$x^{2} y^{5} \frac{y^{6}}{x^{4}}$

Step 8

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

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Step 8.1

Factor $x^{2}$ out of $x^{2} y^{5}$ .

$x^{2} (y^{5}) \frac{y^{6}}{x^{4}}$

Step 8.2

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

$x^{2} (y^{5}) \frac{y^{6}}{x^{2} x^{2}}$

Step 8.3

Cancel the common factor.

$x^{2} y^{5} \frac{y^{6}}{x^{2} x^{2}}$

Step 8.4

Rewrite the expression.

$y^{5} \frac{y^{6}}{x^{2}}$

Step 9

Combine $y^{5}$ and $\frac{y^{6}}{x^{2}}$ .

$\frac{y^{5} y^{6}}{x^{2}}$

Step 10

Multiply $y^{5}$ by $y^{6}$ by adding the exponents.

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Step 10.1

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

$\frac{y^{5 + 6}}{x^{2}}$

Step 10.2

Add $5$ and $6$ .

$\frac{y^{11}}{x^{2}}$