Basic Math Examples

${(64 a^{3})}^{\frac{4}{3}}$

Step 1

Simplify the expression.

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Step 1.1

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

$64^{\frac{4}{3}} {(a^{3})}^{\frac{4}{3}}$

Step 1.2

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

${(4^{3})}^{\frac{4}{3}} {(a^{3})}^{\frac{4}{3}}$

Step 1.3

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

$4^{3 (\frac{4}{3})} {(a^{3})}^{\frac{4}{3}}$

Step 2

Cancel the common factor of $3$ .

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Step 2.1

Cancel the common factor.

$4^{3 (\frac{4}{3})} {(a^{3})}^{\frac{4}{3}}$

Step 2.2

Rewrite the expression.

$4^{4} {(a^{3})}^{\frac{4}{3}}$

Step 3

Simplify the expression.

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Step 3.1

Raise $4$ to the power of $4$ .

$256 {(a^{3})}^{\frac{4}{3}}$

Step 3.2

Multiply the exponents in ${(a^{3})}^{\frac{4}{3}}$ .

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Step 3.2.1

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

$256 a^{3 (\frac{4}{3})}$

Step 3.2.2

Cancel the common factor of $3$ .

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Step 3.2.2.1

Cancel the common factor.

$256 a^{3 (\frac{4}{3})}$

Step 3.2.2.2

Rewrite the expression.

$256 a^{4}$