Evaluate (-5/3)^3

${(- \frac{5}{3})}^{3}$

Step 1

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

Apply the product rule to $- \frac{5}{3}$ .

${(- 1)}^{3} {(\frac{5}{3})}^{3}$

Apply the product rule to $\frac{5}{3}$ .

${(- 1)}^{3} \frac{5^{3}}{3^{3}}$

Step 2

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

$- \frac{5^{3}}{3^{3}}$

Step 3

Raise $5$ to the power of $3$ .

$- \frac{125}{3^{3}}$

Step 4

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

$- \frac{125}{27}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{125}{27}$

Decimal Form:

$- 4.\overline{629}$

Mixed Number Form:

$- 4 \frac{17}{27}$