Calculus Examples

$lim_{x \to c} {(8)}^{\frac{2}{3}}$

Step 1

Evaluate the limit of ${(8)}^{\frac{2}{3}}$ which is constant as $x$ approaches $c$ .

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

Step 2

Simplify the answer.

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

Cancel the common factor of $3$ .

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Step 2.3.1

Cancel the common factor.

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

Step 2.3.2

Rewrite the expression.

$2^{2}$

Step 2.4

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

$4$