Algebra Examples

$f (n) = 10 \cdot 2^{n}$ at $n = - 2$

Step 1

Replace the variable $n$ with $- 2$ in the expression.

$f (- 2) = 10 \cdot 2^{- 2}$

Step 2

Simplify the result.

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Step 2.1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$f (- 2) = 10 \cdot \frac{1}{2^{2}}$

Step 2.2

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

$f (- 2) = 10 \cdot \frac{1}{4}$

Step 2.3

Cancel the common factor of $2$ .

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Step 2.3.1

Factor $2$ out of $10$ .

$f (- 2) = 2 (5) \cdot \frac{1}{4}$

Step 2.3.2

Factor $2$ out of $4$ .

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

Step 2.3.3

Cancel the common factor.

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

Step 2.3.4

Rewrite the expression.

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

Step 2.4

Combine $5$ and $\frac{1}{2}$ .

$f (- 2) = \frac{5}{2}$

Step 2.5

The final answer is $\frac{5}{2}$ .

$\frac{5}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{5}{2}$

Decimal Form:

$2.5$

Mixed Number Form:

$2 \frac{1}{2}$

Step 4