Algebra Examples

${(\frac{x^{2}}{27})}^{\frac{1}{3}}$

Step 1

Apply basic rules of exponents.

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Step 1.1

Apply the product rule to $\frac{x^{2}}{27}$ .

$\frac{{(x^{2})}^{\frac{1}{3}}}{27^{\frac{1}{3}}}$

Step 1.2

Multiply the exponents in ${(x^{2})}^{\frac{1}{3}}$ .

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Step 1.2.1

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

$\frac{x^{2 (\frac{1}{3})}}{27^{\frac{1}{3}}}$

Step 1.2.2

Combine $2$ and $\frac{1}{3}$ .

$\frac{x^{\frac{2}{3}}}{27^{\frac{1}{3}}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $27$ as $3^{3}$ .

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

Step 2.2

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

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

Step 2.3

Cancel the common factor of $3$ .

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Step 2.3.1

Cancel the common factor.

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

Step 2.3.2

Rewrite the expression.

$\frac{x^{\frac{2}{3}}}{3^{1}}$

Step 2.4

Evaluate the exponent.

$\frac{x^{\frac{2}{3}}}{3}$