Algebra Examples

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

Step 1

Simplify the numerator.

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Step 1.1

Apply the product rule to $x^{4} y^{- 3}$ .

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

Step 1.2

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

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Step 1.2.1

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

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

Step 1.2.2

Multiply $4$ by $2$ .

$\frac{x^{8} {(y^{- 3})}^{2}}{x^{3} y^{5}}$

Step 1.3

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

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Step 1.3.1

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

$\frac{x^{8} y^{- 3 \cdot 2}}{x^{3} y^{5}}$

Step 1.3.2

Multiply $- 3$ by $2$ .

$\frac{x^{8} y^{- 6}}{x^{3} y^{5}}$

Step 1.4

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

$\frac{x^{8} \frac{1}{y^{6}}}{x^{3} y^{5}}$

Step 2

Combine $x^{8}$ and $\frac{1}{y^{6}}$ .

$\frac{\frac{x^{8}}{y^{6}}}{x^{3} y^{5}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{x^{8}}{y^{6}} \cdot \frac{1}{x^{3} y^{5}}$

Step 4

Combine.

$\frac{x^{8} \cdot 1}{y^{6} (x^{3} y^{5})}$

Step 5

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

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Step 5.1

Move $y^{5}$ .

$\frac{x^{8} \cdot 1}{y^{5} y^{6} x^{3}}$

Step 5.2

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

$\frac{x^{8} \cdot 1}{y^{5 + 6} x^{3}}$

Step 5.3

Add $5$ and $6$ .

$\frac{x^{8} \cdot 1}{y^{11} x^{3}}$

Step 6

Multiply $x^{8}$ by $1$ .

$\frac{x^{8}}{y^{11} x^{3}}$

Step 7

Cancel the common factor of $x^{8}$ and $x^{3}$ .

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Step 7.1

Factor $x^{3}$ out of $x^{8}$ .

$\frac{x^{3} x^{5}}{y^{11} x^{3}}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $x^{3}$ out of $y^{11} x^{3}$ .

$\frac{x^{3} x^{5}}{x^{3} y^{11}}$

Step 7.2.2

Cancel the common factor.

$\frac{x^{3} x^{5}}{x^{3} y^{11}}$

Step 7.2.3

Rewrite the expression.

$\frac{x^{5}}{y^{11}}$