Algebra Examples

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

Step 1

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

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

Step 2

Simplify the denominator.

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Step 2.1

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

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

Multiply $2$ by $2$ .

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

Step 2.3

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

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Step 2.3.1

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

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

Step 2.3.2

Multiply $3$ by $2$ .

$\frac{1}{x^{4} y^{6}} {(x^{4})}^{2}$

Step 3

Simplify terms.

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Step 3.1

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

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Step 3.1.1

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

$\frac{1}{x^{4} y^{6}} x^{4 \cdot 2}$

Step 3.1.2

Multiply $4$ by $2$ .

$\frac{1}{x^{4} y^{6}} x^{8}$

Step 3.2

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

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Step 3.2.1

Factor $x^{4}$ out of $x^{4} y^{6}$ .

$\frac{1}{x^{4} (y^{6})} x^{8}$

Step 3.2.2

Factor $x^{4}$ out of $x^{8}$ .

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

Step 3.2.3

Cancel the common factor.

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

Step 3.2.4

Rewrite the expression.

$\frac{1}{y^{6}} x^{4}$

Step 3.3

Combine $\frac{1}{y^{6}}$ and $x^{4}$ .

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