Evaluate (1/9)^2*(-3)^3

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

Simplify the expression.

Apply the product rule to $\frac{1}{9}$ .

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

One to any power is one.

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

Raise $9$ to the power of $2$ .

$\frac{1}{81} \cdot {(- 3)}^{3}$

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

$\frac{1}{81} \cdot - 27$

$\frac{1}{81} \cdot - 27$

Cancel the common factor of $27$ .

Factor $27$ out of $81$ .

$\frac{1}{27 (3)} \cdot - 27$

Factor $27$ out of $- 27$ .

$\frac{1}{27 \cdot 3} \cdot (27 \cdot - 1)$

Cancel the common factor.

$\frac{1}{27 \cdot 3} \cdot (27 \cdot - 1)$

Rewrite the expression.

$\frac{1}{3} \cdot - 1$

$\frac{1}{3} \cdot - 1$

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

$\frac{- 1}{3}$

Move the negative in front of the fraction.

$- \frac{1}{3}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{3}$

Decimal Form:

$- 0.\overline{3}$

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