Basic Math Examples

${(64 b^{3})}^{\frac{1}{3}}$

Step 1

Simplify the expression.

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Step 1.1

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

$64^{\frac{1}{3}} {(b^{3})}^{\frac{1}{3}}$

Step 1.2

Rewrite $64$ as $4^{3}$ .

${(4^{3})}^{\frac{1}{3}} {(b^{3})}^{\frac{1}{3}}$

Step 1.3

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

$4^{3 (\frac{1}{3})} {(b^{3})}^{\frac{1}{3}}$

Step 2

Cancel the common factor of $3$ .

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Step 2.1

Cancel the common factor.

$4^{3 (\frac{1}{3})} {(b^{3})}^{\frac{1}{3}}$

Step 2.2

Rewrite the expression.

$4^{1} {(b^{3})}^{\frac{1}{3}}$

Step 3

Simplify the expression.

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Step 3.1

Evaluate the exponent.

$4 {(b^{3})}^{\frac{1}{3}}$

Step 3.2

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

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Step 3.2.1

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

$4 b^{3 (\frac{1}{3})}$

Step 3.2.2

Cancel the common factor of $3$ .

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Step 3.2.2.1

Cancel the common factor.

$4 b^{3 (\frac{1}{3})}$

Step 3.2.2.2

Rewrite the expression.

$4 b^{1}$

Step 4

Simplify.

$4 b$