Algebra Examples

$[- 5 {(\frac{1}{5})}^{n}]$

Step 1

Substitute in the value of $n$ to find the $n$ th term.

$a_{2} = - 5 {(\frac{1}{5})}^{2}$

Step 2

Simplify the expression.

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Step 2.1

Remove parentheses.

$a_{2} = - 5 {(\frac{1}{5})}^{2}$

Step 2.2

Apply the product rule to $\frac{1}{5}$ .

$a_{2} = - 5 \frac{1^{2}}{5^{2}}$

Step 2.3

One to any power is one.

$a_{2} = - 5 \frac{1}{5^{2}}$

Step 2.4

Raise $5$ to the power of $2$ .

$a_{2} = - 5 (\frac{1}{25})$

Step 3

Cancel the common factor of $5$ .

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Step 3.1

Factor $5$ out of $- 5$ .

$a_{2} = 5 (- 1) (\frac{1}{25})$

Step 3.2

Factor $5$ out of $25$ .

$a_{2} = 5 \cdot (- 1 \frac{1}{5 \cdot 5})$

Step 3.3

Cancel the common factor.

$a_{2} = 5 \cdot (- 1 \frac{1}{5 \cdot 5})$

Step 3.4

Rewrite the expression.

$a_{2} = - 1 (\frac{1}{5})$

Step 4

Rewrite $- 1 (\frac{1}{5})$ as $- (\frac{1}{5})$ .

$a_{2} = - \frac{1}{5}$