Algebra Examples

$f (x) = {(\frac{1}{3})}^{x}$

Step 1

Substitute $- 2$ for $x$ and find the result for $y$ .

$y = {(\frac{1}{3})}^{- 2}$

Step 2

Solve the equation for $y$ .

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Step 2.1

Remove parentheses.

$y = {(\frac{1}{3})}^{- 2}$

Step 2.2

Simplify ${(\frac{1}{3})}^{- 2}$ .

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Step 2.2.1

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

$y = 3^{2}$

Step 2.2.2

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

$y = 9$

Step 3

Substitute $- 1$ for $x$ and find the result for $y$ .

$y = {(\frac{1}{3})}^{- 1}$

Step 4

Solve the equation for $y$ .

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Step 4.1

Remove parentheses.

$y = {(\frac{1}{3})}^{- 1}$

Step 4.2

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

$y = 3$

Step 5

Substitute $0$ for $x$ and find the result for $y$ .

$y = {(\frac{1}{3})}^{0}$

Step 6

Solve the equation for $y$ .

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Step 6.1

Remove parentheses.

$y = {(\frac{1}{3})}^{0}$

Step 6.2

Simplify ${(\frac{1}{3})}^{0}$ .

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Step 6.2.1

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

$y = \frac{1^{0}}{3^{0}}$

Step 6.2.2

Anything raised to $0$ is $1$ .

$y = \frac{1}{3^{0}}$

Step 6.2.3

Anything raised to $0$ is $1$ .

$y = \frac{1}{1}$

Step 6.2.4

Divide $1$ by $1$ .

$y = 1$

Step 7

Substitute $1$ for $x$ and find the result for $y$ .

$y = {(\frac{1}{3})}^{1}$

Step 8

Solve the equation for $y$ .

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Step 8.1

Remove parentheses.

$y = \frac{1}{3}$

Step 8.2

Remove parentheses.

$y = \frac{1}{3}$

Step 9

Substitute $2$ for $x$ and find the result for $y$ .

$y = {(\frac{1}{3})}^{2}$

Step 10

Solve the equation for $y$ .

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Step 10.1

Remove parentheses.

$y = {(\frac{1}{3})}^{2}$

Step 10.2

Simplify ${(\frac{1}{3})}^{2}$ .

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Step 10.2.1

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

$y = \frac{1^{2}}{3^{2}}$

Step 10.2.2

One to any power is one.

$y = \frac{1}{3^{2}}$

Step 10.2.3

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

$y = \frac{1}{9}$

Step 11

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 2 & 9 \\ - 1 & 3 \\ 0 & 1 \\ 1 & \frac{1}{3} \\ 2 & \frac{1}{9} \end{array}$

Step 12