Algebra Examples

${(x^{16} y^{20} z^{8})}^{\frac{1}{4}}$

Step 1

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

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Step 1.1

Apply the product rule to $x^{16} y^{20} z^{8}$ .

${(x^{16} y^{20})}^{\frac{1}{4}} {(z^{8})}^{\frac{1}{4}}$

Step 1.2

Apply the product rule to $x^{16} y^{20}$ .

${(x^{16})}^{\frac{1}{4}} {(y^{20})}^{\frac{1}{4}} {(z^{8})}^{\frac{1}{4}}$

Step 2

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

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Step 2.1

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

$x^{16 (\frac{1}{4})} {(y^{20})}^{\frac{1}{4}} {(z^{8})}^{\frac{1}{4}}$

Step 2.2

Cancel the common factor of $4$ .

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Step 2.2.1

Factor $4$ out of $16$ .

$x^{4 (4) \frac{1}{4}} {(y^{20})}^{\frac{1}{4}} {(z^{8})}^{\frac{1}{4}}$

Step 2.2.2

Cancel the common factor.

$x^{4 \cdot 4 \frac{1}{4}} {(y^{20})}^{\frac{1}{4}} {(z^{8})}^{\frac{1}{4}}$

Step 2.2.3

Rewrite the expression.

$x^{4} {(y^{20})}^{\frac{1}{4}} {(z^{8})}^{\frac{1}{4}}$

Step 3

Multiply the exponents in ${(y^{20})}^{\frac{1}{4}}$ .

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Step 3.1

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

$x^{4} y^{20 (\frac{1}{4})} {(z^{8})}^{\frac{1}{4}}$

Step 3.2

Cancel the common factor of $4$ .

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Step 3.2.1

Factor $4$ out of $20$ .

$x^{4} y^{4 (5) \frac{1}{4}} {(z^{8})}^{\frac{1}{4}}$

Step 3.2.2

Cancel the common factor.

$x^{4} y^{4 \cdot 5 \frac{1}{4}} {(z^{8})}^{\frac{1}{4}}$

Step 3.2.3

Rewrite the expression.

$x^{4} y^{5} {(z^{8})}^{\frac{1}{4}}$

Step 4

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

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Step 4.1

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

$x^{4} y^{5} z^{8 (\frac{1}{4})}$

Step 4.2

Cancel the common factor of $4$ .

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Step 4.2.1

Factor $4$ out of $8$ .

$x^{4} y^{5} z^{4 (2) \frac{1}{4}}$

Step 4.2.2

Cancel the common factor.

$x^{4} y^{5} z^{4 \cdot 2 \frac{1}{4}}$

Step 4.2.3

Rewrite the expression.

$x^{4} y^{5} z^{2}$