Evaluate the Function g(x)=1/5*(1/3)^x at x=3

$g (x) = \frac{1}{5} \cdot {(\frac{1}{3})}^{x}$ at $x = 3$

Replace the variable $x$ with $3$ in the expression.

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

Simplify the result.

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

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

Combine.

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

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

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

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

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

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

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

Add $1$ and $3$ .

$g (3) = \frac{1^{4}}{5 \cdot 3^{3}}$

One to any power is one.

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

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

$g (3) = \frac{1}{5 \cdot 27}$

Multiply $5$ by $27$ .

$g (3) = \frac{1}{135}$

The final answer is $\frac{1}{135}$ .

$\frac{1}{135}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{135}$

Decimal Form:

$0.0\overline{074}$