Evaluate 1/5*(1/3)^3

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

Step 1

Apply the product rule to $\frac{1}{3}$ .

$\frac{1}{5} \cdot \frac{1^{3}}{3^{3}}$

Step 2

Combine.

$\frac{1 \cdot 1^{3}}{5 \cdot 3^{3}}$

Step 3

Multiply $1$ by $1^{3}$ by adding the exponents.

Multiply $1$ by $1^{3}$ .

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

$\frac{1^{1} \cdot 1^{3}}{5 \cdot 3^{3}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1^{1 + 3}}{5 \cdot 3^{3}}$

Add $1$ and $3$ .

$\frac{1^{4}}{5 \cdot 3^{3}}$

Step 4

One to any power is one.

$\frac{1}{5 \cdot 3^{3}}$

Step 5

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

$\frac{1}{5 \cdot 27}$

Step 6

Multiply $5$ by $27$ .

$\frac{1}{135}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{135}$

Decimal Form:

$0.0\overline{074}$