Evaluate 8^(2/3)+8^(-2/3)

$8^{\frac{2}{3}} + 8^{- \frac{2}{3}}$

Step 1

Simplify each term.

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

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

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$2^{2} + 8^{- \frac{2}{3}}$

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

$4 + 8^{- \frac{2}{3}}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$4 + \frac{1}{8^{\frac{2}{3}}}$

Simplify the denominator.

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

$4 + \frac{1}{{(2^{3})}^{\frac{2}{3}}}$

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

$4 + \frac{1}{2^{3 (\frac{2}{3})}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$4 + \frac{1}{2^{3 (\frac{2}{3})}}$

Rewrite the expression.

$4 + \frac{1}{2^{2}}$

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

$4 + \frac{1}{4}$

Step 2

To write $4$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$4 \cdot \frac{4}{4} + \frac{1}{4}$

Step 3

Combine $4$ and $\frac{4}{4}$ .

$\frac{4 \cdot 4}{4} + \frac{1}{4}$

Step 4

Combine the numerators over the common denominator.

$\frac{4 \cdot 4 + 1}{4}$

Step 5

Simplify the numerator.

Multiply $4$ by $4$ .

$\frac{16 + 1}{4}$

Add $16$ and $1$ .

$\frac{17}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{17}{4}$

Decimal Form:

$4.25$

Mixed Number Form:

$4 \frac{1}{4}$

Evaluate 8^(2/3)+8^(-2/3)

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