Algebra Examples

$f (- 2) = {(\frac{2}{3})}^{x}$

Step 1

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

$f (- 2) = {(\frac{2}{3})}^{- 2}$

Step 2

Simplify the result.

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Step 2.1

Change the sign of the exponent by rewriting the base as its reciprocal.

$f (- 2) = {(\frac{3}{2})}^{2}$

Step 2.2

Apply the product rule to $\frac{3}{2}$ .

$f (- 2) = \frac{3^{2}}{2^{2}}$

Step 2.3

Raise $3$ to the power of $2$ .

$f (- 2) = \frac{9}{2^{2}}$

Step 2.4

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

$f (- 2) = \frac{9}{4}$

Step 2.5

The final answer is $\frac{9}{4}$ .

$\frac{9}{4}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{9}{4}$

Decimal Form:

$2.25$

Mixed Number Form:

$2 \frac{1}{4}$

Step 4