Algebra Examples

${(\frac{x^{8} y^{5}}{x^{9} y^{3}})}^{- 6}$

Step 1

Cancel the common factor of $x^{8}$ and $x^{9}$ .

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Step 1.1

Factor $x^{8}$ out of $x^{8} y^{5}$ .

${(\frac{x^{8} (y^{5})}{x^{9} y^{3}})}^{- 6}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $x^{8}$ out of $x^{9} y^{3}$ .

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

Step 2

Cancel the common factor of $y^{5}$ and $y^{3}$ .

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Step 2.1

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

${(\frac{y^{3} y^{2}}{x y^{3}})}^{- 6}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

${(\frac{y^{3} y^{2}}{y^{3} x})}^{- 6}$

Step 2.2.2

Cancel the common factor.

${(\frac{y^{3} y^{2}}{y^{3} x})}^{- 6}$

Step 2.2.3

Rewrite the expression.

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

Step 3

Change the sign of the exponent by rewriting the base as its reciprocal.

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

Step 4

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

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

Step 5

Multiply the exponents in ${(y^{2})}^{6}$ .

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Step 5.1

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

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

Step 5.2

Multiply $2$ by $6$ .

$\frac{x^{6}}{y^{12}}$