Algebra Examples

${(64 x^{3} y^{- 12})}^{\frac{1}{6}}$

Step 1

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

${(64 x^{3} \frac{1}{y^{12}})}^{\frac{1}{6}}$

Step 2

Multiply $64 x^{3} \frac{1}{y^{12}}$ .

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Step 2.1

Combine $64$ and $\frac{1}{y^{12}}$ .

${(x^{3} \frac{64}{y^{12}})}^{\frac{1}{6}}$

Step 2.2

Combine $x^{3}$ and $\frac{64}{y^{12}}$ .

${(\frac{x^{3} \cdot 64}{y^{12}})}^{\frac{1}{6}}$

Step 3

Move $64$ to the left of $x^{3}$ .

${(\frac{64 \cdot x^{3}}{y^{12}})}^{\frac{1}{6}}$

Step 4

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

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Step 4.1

Apply the product rule to $\frac{64 x^{3}}{y^{12}}$ .

$\frac{{(64 x^{3})}^{\frac{1}{6}}}{{(y^{12})}^{\frac{1}{6}}}$

Step 4.2

Apply the product rule to $64 x^{3}$ .

$\frac{64^{\frac{1}{6}} {(x^{3})}^{\frac{1}{6}}}{{(y^{12})}^{\frac{1}{6}}}$

Step 5

Simplify the numerator.

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Step 5.1

Rewrite $64$ as $2^{6}$ .

$\frac{{(2^{6})}^{\frac{1}{6}} {(x^{3})}^{\frac{1}{6}}}{{(y^{12})}^{\frac{1}{6}}}$

Step 5.2

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

$\frac{2^{6 (\frac{1}{6})} {(x^{3})}^{\frac{1}{6}}}{{(y^{12})}^{\frac{1}{6}}}$

Step 5.3

Cancel the common factor of $6$ .

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Step 5.3.1

Cancel the common factor.

$\frac{2^{6 (\frac{1}{6})} {(x^{3})}^{\frac{1}{6}}}{{(y^{12})}^{\frac{1}{6}}}$

Step 5.3.2

Rewrite the expression.

$\frac{2^{1} {(x^{3})}^{\frac{1}{6}}}{{(y^{12})}^{\frac{1}{6}}}$

Step 5.4

Evaluate the exponent.

$\frac{2 {(x^{3})}^{\frac{1}{6}}}{{(y^{12})}^{\frac{1}{6}}}$

Step 5.5

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

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Step 5.5.1

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

$\frac{2 x^{3 (\frac{1}{6})}}{{(y^{12})}^{\frac{1}{6}}}$

Step 5.5.2

Cancel the common factor of $3$ .

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Step 5.5.2.1

Factor $3$ out of $6$ .

$\frac{2 x^{3 \frac{1}{3 (2)}}}{{(y^{12})}^{\frac{1}{6}}}$

Step 5.5.2.2

Cancel the common factor.

$\frac{2 x^{3 \frac{1}{3 \cdot 2}}}{{(y^{12})}^{\frac{1}{6}}}$

Step 5.5.2.3

Rewrite the expression.

$\frac{2 x^{\frac{1}{2}}}{{(y^{12})}^{\frac{1}{6}}}$

Step 6

Multiply the exponents in ${(y^{12})}^{\frac{1}{6}}$ .

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Step 6.1

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

$\frac{2 x^{\frac{1}{2}}}{y^{12 (\frac{1}{6})}}$

Step 6.2

Cancel the common factor of $6$ .

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Step 6.2.1

Factor $6$ out of $12$ .

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

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