Algebra Examples

${(\frac{x^{8}}{z^{16}})}^{\frac{1}{4}}$

Step 1

Apply the product rule to $\frac{x^{8}}{z^{16}}$ .

$\frac{{(x^{8})}^{\frac{1}{4}}}{{(z^{16})}^{\frac{1}{4}}}$

Step 2

Multiply the exponents in ${(x^{8})}^{\frac{1}{4}}$ .

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Step 2.1

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

$\frac{x^{8 (\frac{1}{4})}}{{(z^{16})}^{\frac{1}{4}}}$

Step 2.2

Cancel the common factor of $4$ .

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Step 2.2.1

Factor $4$ out of $8$ .

$\frac{x^{4 (2) \frac{1}{4}}}{{(z^{16})}^{\frac{1}{4}}}$

Step 2.2.2

Cancel the common factor.

$\frac{x^{4 \cdot 2 \frac{1}{4}}}{{(z^{16})}^{\frac{1}{4}}}$

Step 2.2.3

Rewrite the expression.

$\frac{x^{2}}{{(z^{16})}^{\frac{1}{4}}}$

Step 3

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

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Step 3.1

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

$\frac{x^{2}}{z^{16 (\frac{1}{4})}}$

Step 3.2

Cancel the common factor of $4$ .

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Step 3.2.1

Factor $4$ out of $16$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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