Evaluate (4/3)^(3(-1/2))

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

Multiply $3 (- \frac{1}{2})$ .

Multiply $- 1$ by $3$ .

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

Combine $- 3$ and $\frac{1}{2}$ .

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

Move the negative in front of the fraction.

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

Change the sign of the exponent by rewriting the base as its reciprocal.

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

Apply the product rule to $\frac{3}{4}$ .

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

Simplify the denominator.

Rewrite $4$ as $2^{2}$ .

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Raise $2$ to the power of $3$ .

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.64951905 \dots$