Precalculus Examples

${(16 x^{4} y^{6})}^{- \frac{3}{2}}$

Step 1

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

$\frac{1}{{(16 x^{4} y^{6})}^{\frac{3}{2}}}$

Step 2

Simplify the denominator.

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Step 2.1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 2.1.1

Apply the product rule to $16 x^{4} y^{6}$ .

$\frac{1}{{(16 x^{4})}^{\frac{3}{2}} {(y^{6})}^{\frac{3}{2}}}$

Step 2.1.2

Apply the product rule to $16 x^{4}$ .

$\frac{1}{16^{\frac{3}{2}} {(x^{4})}^{\frac{3}{2}} {(y^{6})}^{\frac{3}{2}}}$

Step 2.2

Rewrite $16$ as $4^{2}$ .

$\frac{1}{{(4^{2})}^{\frac{3}{2}} {(x^{4})}^{\frac{3}{2}} {(y^{6})}^{\frac{3}{2}}}$

Step 2.3

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

$\frac{1}{4^{2 (\frac{3}{2})} {(x^{4})}^{\frac{3}{2}} {(y^{6})}^{\frac{3}{2}}}$

Step 2.4

Cancel the common factor of $2$ .

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Step 2.4.1

Cancel the common factor.

$\frac{1}{4^{2 (\frac{3}{2})} {(x^{4})}^{\frac{3}{2}} {(y^{6})}^{\frac{3}{2}}}$

Step 2.4.2

Rewrite the expression.

$\frac{1}{4^{3} {(x^{4})}^{\frac{3}{2}} {(y^{6})}^{\frac{3}{2}}}$

Step 2.5

Raise $4$ to the power of $3$ .

$\frac{1}{64 {(x^{4})}^{\frac{3}{2}} {(y^{6})}^{\frac{3}{2}}}$

Step 2.6

Multiply the exponents in ${(x^{4})}^{\frac{3}{2}}$ .

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Step 2.6.1

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

$\frac{1}{64 x^{4 (\frac{3}{2})} {(y^{6})}^{\frac{3}{2}}}$

Step 2.6.2

Cancel the common factor of $2$ .

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Step 2.6.2.1

Factor $2$ out of $4$ .

$\frac{1}{64 x^{2 (2) \frac{3}{2}} {(y^{6})}^{\frac{3}{2}}}$

Step 2.6.2.2

Cancel the common factor.

$\frac{1}{64 x^{2 \cdot 2 \frac{3}{2}} {(y^{6})}^{\frac{3}{2}}}$

Step 2.6.2.3

Rewrite the expression.

$\frac{1}{64 x^{2 \cdot 3} {(y^{6})}^{\frac{3}{2}}}$

Step 2.6.3

Multiply $2$ by $3$ .

$\frac{1}{64 x^{6} {(y^{6})}^{\frac{3}{2}}}$

Step 2.7

Multiply the exponents in ${(y^{6})}^{\frac{3}{2}}$ .

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Step 2.7.1

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

$\frac{1}{64 x^{6} y^{6 (\frac{3}{2})}}$

Step 2.7.2

Cancel the common factor of $2$ .

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Step 2.7.2.1

Factor $2$ out of $6$ .

$\frac{1}{64 x^{6} y^{2 (3) \frac{3}{2}}}$

Step 2.7.2.2

Cancel the common factor.

$\frac{1}{64 x^{6} y^{2 \cdot 3 \frac{3}{2}}}$

Step 2.7.2.3

Rewrite the expression.

$\frac{1}{64 x^{6} y^{3 \cdot 3}}$

Step 2.7.3

Multiply $3$ by $3$ .

$\frac{1}{64 x^{6} y^{9}}$