Evaluate 64^(1/3)+9^(-1/2)

$64^{\frac{1}{3}} + 9^{- \frac{1}{2}}$

Simplify each term.

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

${(4^{3})}^{\frac{1}{3}} + 9^{- \frac{1}{2}}$

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

$4^{3 (\frac{1}{3})} + 9^{- \frac{1}{2}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$4^{3 (\frac{1}{3})} + 9^{- \frac{1}{2}}$

Rewrite the expression.

$4^{1} + 9^{- \frac{1}{2}}$

Evaluate the exponent.

$4 + 9^{- \frac{1}{2}}$

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

$4 + \frac{1}{9^{\frac{1}{2}}}$

Simplify the denominator.

Rewrite $9$ as $3^{2}$ .

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Evaluate the exponent.

$4 + \frac{1}{3}$

To write $4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$4 \cdot \frac{3}{3} + \frac{1}{3}$

Combine $4$ and $\frac{3}{3}$ .

$\frac{4 \cdot 3}{3} + \frac{1}{3}$

Combine the numerators over the common denominator.

$\frac{4 \cdot 3 + 1}{3}$

Simplify the numerator.

Multiply $4$ by $3$ .

$\frac{12 + 1}{3}$

Add $12$ and $1$ .

$\frac{13}{3}$

The result can be shown in multiple forms.

Exact Form:

$\frac{13}{3}$

Decimal Form:

$4.\overline{3}$

Mixed Number Form:

$4 \frac{1}{3}$