Precalculus Examples

${(\frac{16 x^{- 10}}{x^{6}})}^{- \frac{1}{4}}$

Step 1

Move $x^{- 10}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{16}{x^{6} x^{10}})}^{- \frac{1}{4}}$

Step 2

Multiply $x^{6}$ by $x^{10}$ by adding the exponents.

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Step 2.1

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

${(\frac{16}{x^{6 + 10}})}^{- \frac{1}{4}}$

Step 2.2

Add $6$ and $10$ .

${(\frac{16}{x^{16}})}^{- \frac{1}{4}}$

Step 3

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

${(\frac{x^{16}}{16})}^{\frac{1}{4}}$

Step 4

Apply basic rules of exponents.

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Step 4.1

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

$\frac{{(x^{16})}^{\frac{1}{4}}}{16^{\frac{1}{4}}}$

Step 4.2

Multiply the exponents in ${(x^{16})}^{\frac{1}{4}}$ .

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Step 4.2.1

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

$\frac{x^{16 (\frac{1}{4})}}{16^{\frac{1}{4}}}$

Step 4.2.2

Cancel the common factor of $4$ .

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Step 4.2.2.1

Factor $4$ out of $16$ .

$\frac{x^{4 (4) \frac{1}{4}}}{16^{\frac{1}{4}}}$

Step 4.2.2.2

Cancel the common factor.

$\frac{x^{4 \cdot 4 \frac{1}{4}}}{16^{\frac{1}{4}}}$

Step 4.2.2.3

Rewrite the expression.

$\frac{x^{4}}{16^{\frac{1}{4}}}$

Step 5

Simplify the denominator.

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Step 5.1

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

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

Step 5.2

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

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

Step 5.3

Cancel the common factor of $4$ .

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Step 5.3.1

Cancel the common factor.

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

Step 5.3.2

Rewrite the expression.

$\frac{x^{4}}{2^{1}}$

Step 5.4

Evaluate the exponent.

$\frac{x^{4}}{2}$