Evaluate (-1/2*3)^3

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

Step 1

Multiply $- \frac{1}{2} \cdot 3$ .

Multiply $3$ by $- 1$ .

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

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

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

Step 2

Move the negative in front of the fraction.

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

Step 3

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

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

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

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

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

Step 4

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

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

Step 5

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

$- \frac{27}{2^{3}}$

Step 6

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

$- \frac{27}{8}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{27}{8}$

Decimal Form:

$- 3.375$

Mixed Number Form:

$- 3 \frac{3}{8}$