Algebra Examples

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

Step 1

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

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

Step 2

Simplify the result.

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Step 2.1

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

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

Step 2.2

Combine.

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

Step 2.3

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

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Step 2.3.1

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

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Step 2.3.1.1

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

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

Step 2.3.1.2

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

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

Step 2.3.2

Add $1$ and $3$ .

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

Step 2.4

One to any power is one.

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

Step 2.5

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

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

Step 2.6

Multiply $5$ by $27$ .

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

Step 2.7

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

$\frac{1}{135}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{135}$

Decimal Form:

$0.0\overline{074}$

Step 4