Calculus Examples

$lim_{x \to c} {(64)}^{\frac{2}{3}}$

Step 1

Evaluate the limit of ${(64)}^{\frac{2}{3}}$ which is constant as $x$ approaches $c$ .

${(64)}^{\frac{2}{3}}$

Step 2

Simplify the answer.

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Step 2.1

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

${(4^{3})}^{\frac{2}{3}}$

Step 2.2

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

$4^{3 (\frac{2}{3})}$

Step 2.3

Cancel the common factor of $3$ .

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Step 2.3.1

Cancel the common factor.

$4^{3 (\frac{2}{3})}$

Step 2.3.2

Rewrite the expression.

$4^{2}$

Step 2.4

Raise $4$ to the power of $2$ .

$16$