Algebra Examples

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

Step 1

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

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Step 1.1

Move $x^{2}$ .

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

Step 1.2

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

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

Step 1.3

Subtract $3$ from $2$ .

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

Step 2

Multiply $y^{- 4}$ by $y^{3}$ by adding the exponents.

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Step 2.1

Move $y^{3}$ .

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

Step 2.2

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

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

Step 2.3

Subtract $4$ from $3$ .

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

Step 3

Simplify the expression.

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

Move ${(y^{3})}^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 3.4

Multiply the exponents in ${(y^{3})}^{4}$ .

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Step 3.4.1

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

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

Step 3.4.2

Multiply $3$ by $4$ .

$\frac{y^{12}}{x y}$

Step 4

Cancel the common factor of $y^{12}$ and $y$ .

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Step 4.1

Factor $y$ out of $y^{12}$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $y$ out of $x y$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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