Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Combine $x^{2}$ and $\frac{1}{y^{3}}$ .

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

Step 4

Apply basic rules of exponents.

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Step 4.1

Apply the product rule to $\frac{x^{2}}{y^{3}}$ .

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

Step 4.2

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

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Step 4.2.1

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

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

Step 4.2.2

Multiply $2$ by $2$ .

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

Step 4.3

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

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Step 4.3.1

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

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

Step 4.3.2

Multiply $3$ by $2$ .

$\frac{x^{4}}{y^{6}} {(x^{- 1} y^{4})}^{3}$

Step 5

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

$\frac{x^{4}}{y^{6}} {(\frac{1}{x} y^{4})}^{3}$

Step 6

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

$\frac{x^{4}}{y^{6}} {(\frac{y^{4}}{x})}^{3}$

Step 7

Apply the product rule to $\frac{y^{4}}{x}$ .

$\frac{x^{4}}{y^{6}} \cdot \frac{{(y^{4})}^{3}}{x^{3}}$

Step 8

Combine.

$\frac{x^{4} {(y^{4})}^{3}}{y^{6} x^{3}}$

Step 9

Cancel the common factor of $x^{4}$ and $x^{3}$ .

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Step 9.1

Factor $x^{3}$ out of $x^{4} {(y^{4})}^{3}$ .

$\frac{x^{3} (x {(y^{4})}^{3})}{y^{6} x^{3}}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $x^{3}$ out of $y^{6} x^{3}$ .

$\frac{x^{3} (x {(y^{4})}^{3})}{x^{3} y^{6}}$

Step 9.2.2

Cancel the common factor.

$\frac{x^{3} (x {(y^{4})}^{3})}{x^{3} y^{6}}$

Step 9.2.3

Rewrite the expression.

$\frac{x {(y^{4})}^{3}}{y^{6}}$

Step 10

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

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Step 10.1

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

$\frac{x y^{4 \cdot 3}}{y^{6}}$

Step 10.2

Multiply $4$ by $3$ .

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

Step 11

Cancel the common factor of $y^{12}$ and $y^{6}$ .

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Step 11.1

Factor $y^{6}$ out of $x y^{12}$ .

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

Step 11.2

Cancel the common factors.

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Step 11.2.1

Multiply by $1$ .

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

Step 11.2.2

Cancel the common factor.

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

Step 11.2.3

Rewrite the expression.

$\frac{x y^{6}}{1}$

Step 11.2.4

Divide $x y^{6}$ by $1$ .

$x y^{6}$