Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Combine $\frac{1}{x^{2}}$ and $y^{4}$ .

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

Step 4

Apply basic rules of exponents.

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Step 4.1

Apply the product rule to $\frac{y^{4}}{x^{2}}$ .

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

Step 4.2

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

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Step 4.2.1

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

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

Step 4.2.2

Multiply $4$ by $3$ .

$\frac{y^{12}}{{(x^{2})}^{3}} {(x y)}^{3}$

Step 4.3

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

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Step 4.3.1

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

$\frac{y^{12}}{x^{2 \cdot 3}} {(x y)}^{3}$

Step 4.3.2

Multiply $2$ by $3$ .

$\frac{y^{12}}{x^{6}} {(x y)}^{3}$

Step 4.4

Apply the product rule to $x y$ .

$\frac{y^{12}}{x^{6}} (x^{3} y^{3})$

Step 5

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

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Step 5.1

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

$\frac{y^{12}}{x^{3} x^{3}} (x^{3} y^{3})$

Step 5.2

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

$\frac{y^{12}}{x^{3} x^{3}} (x^{3} (y^{3}))$

Step 5.3

Cancel the common factor.

$\frac{y^{12}}{x^{3} x^{3}} (x^{3} y^{3})$

Step 5.4

Rewrite the expression.

$\frac{y^{12}}{x^{3}} y^{3}$

Step 6

Combine $\frac{y^{12}}{x^{3}}$ and $y^{3}$ .

$\frac{y^{12} y^{3}}{x^{3}}$

Step 7

Multiply $y^{12}$ by $y^{3}$ by adding the exponents.

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Step 7.1

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

$\frac{y^{12 + 3}}{x^{3}}$

Step 7.2

Add $12$ and $3$ .

$\frac{y^{15}}{x^{3}}$