Evaluate the Function f(3)=(1/6)^x

$f (3) = {(\frac{1}{6})}^{x}$

Step 1

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

$f (3) = {(\frac{1}{6})}^{3}$

Step 2

Simplify the result.

Apply the product rule to $\frac{1}{6}$ .

$f (3) = \frac{1^{3}}{6^{3}}$

One to any power is one.

$f (3) = \frac{1}{6^{3}}$

Raise $6$ to the power of $3$ .

$f (3) = \frac{1}{216}$

The final answer is $\frac{1}{216}$ .

$\frac{1}{216}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{216}$

Decimal Form:

$0.004\overline{629}$

Step 4