Algebra Examples

Evaluate the exponential function $f (x) = 5^{2 x}$ when $x = - 1$

Step 1

Replace the variable $x$ with $- 1$ in the expression.

$f (- 1) = 5^{2 (- 1)}$

Step 2

Simplify the result.

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Step 2.1

Multiply $2$ by $- 1$ .

$f (- 1) = 5^{- 2}$

Step 2.2

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

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

Step 2.3

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

$f (- 1) = \frac{1}{25}$

Step 2.4

The final answer is $\frac{1}{25}$ .

$\frac{1}{25}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{25}$

Decimal Form:

$0.04$

Step 4