Trigonometry Examples

${(8 x^{2})}^{\frac{1}{3}}$

Step 1

Simplify the expression.

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Step 1.1

Apply the product rule to $8 x^{2}$ .

$8^{\frac{1}{3}} {(x^{2})}^{\frac{1}{3}}$

Step 1.2

Rewrite $8$ as $2^{3}$ .

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

Step 1.3

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

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

Step 2

Cancel the common factor of $3$ .

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Step 2.1

Cancel the common factor.

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

Step 2.2

Rewrite the expression.

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

Step 3

Evaluate the exponent.

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

Step 4

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

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Step 4.1

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

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

Step 4.2

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

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