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

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

Apply the product rule to $\frac{2}{3}$ .

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

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

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

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

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

Multiply $2 (\frac{4}{9})$ .

Combine $2$ and $\frac{4}{9}$ .

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

Multiply $2$ by $4$ .

$\frac{8}{9} {(- \frac{1}{2})}^{3}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $- \frac{1}{2}$ .

$\frac{8}{9} ({(- 1)}^{3} {(\frac{1}{2})}^{3})$

Apply the product rule to $\frac{1}{2}$ .

$\frac{8}{9} ({(- 1)}^{3} \frac{1^{3}}{2^{3}})$

Simplify the expression.

Raise $- 1$ to the power of $3$ .

$\frac{8}{9} (- \frac{1^{3}}{2^{3}})$

One to any power is one.

$\frac{8}{9} (- \frac{1}{2^{3}})$

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

$\frac{8}{9} (- \frac{1}{8})$

Cancel the common factor of $8$ .

Move the leading negative in $- \frac{1}{8}$ into the numerator.

$\frac{8}{9} \cdot \frac{- 1}{8}$

Cancel the common factor.

$\frac{8}{9} \cdot \frac{- 1}{8}$

Rewrite the expression.

$\frac{1}{9} \cdot - 1$

Combine $\frac{1}{9}$ and $- 1$ .

$\frac{- 1}{9}$

Move the negative in front of the fraction.

$- \frac{1}{9}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{9}$

Decimal Form:

$- 0.\overline{1}$