Algebra Examples

${(36 x^{2} y^{3} z)}^{\frac{1}{6}}$

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 $36 x^{2} y^{3} z$ .

${(36 x^{2} y^{3})}^{\frac{1}{6}} z^{\frac{1}{6}}$

Step 1.2

Apply the product rule to $36 x^{2} y^{3}$ .

${(36 x^{2})}^{\frac{1}{6}} {(y^{3})}^{\frac{1}{6}} z^{\frac{1}{6}}$

Step 1.3

Apply the product rule to $36 x^{2}$ .

$36^{\frac{1}{6}} {(x^{2})}^{\frac{1}{6}} {(y^{3})}^{\frac{1}{6}} z^{\frac{1}{6}}$

Step 2

Multiply the exponents in ${(x^{2})}^{\frac{1}{6}}$ .

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Step 2.1

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

$36^{\frac{1}{6}} x^{2 (\frac{1}{6})} {(y^{3})}^{\frac{1}{6}} z^{\frac{1}{6}}$

Step 2.2

Cancel the common factor of $2$ .

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Step 2.2.1

Factor $2$ out of $6$ .

$36^{\frac{1}{6}} x^{2 \frac{1}{2 (3)}} {(y^{3})}^{\frac{1}{6}} z^{\frac{1}{6}}$

Step 2.2.2

Cancel the common factor.

$36^{\frac{1}{6}} x^{2 \frac{1}{2 \cdot 3}} {(y^{3})}^{\frac{1}{6}} z^{\frac{1}{6}}$

Step 2.2.3

Rewrite the expression.

$36^{\frac{1}{6}} x^{\frac{1}{3}} {(y^{3})}^{\frac{1}{6}} z^{\frac{1}{6}}$

Step 3

Multiply the exponents in ${(y^{3})}^{\frac{1}{6}}$ .

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Step 3.1

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

$36^{\frac{1}{6}} x^{\frac{1}{3}} y^{3 (\frac{1}{6})} z^{\frac{1}{6}}$

Step 3.2

Cancel the common factor of $3$ .

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Step 3.2.1

Factor $3$ out of $6$ .

$36^{\frac{1}{6}} x^{\frac{1}{3}} y^{3 \frac{1}{3 (2)}} z^{\frac{1}{6}}$

Step 3.2.2

Cancel the common factor.

$36^{\frac{1}{6}} x^{\frac{1}{3}} y^{3 \frac{1}{3 \cdot 2}} z^{\frac{1}{6}}$

Step 3.2.3

Rewrite the expression.

$36^{\frac{1}{6}} x^{\frac{1}{3}} y^{\frac{1}{2}} z^{\frac{1}{6}}$