Algebra Examples

$2 {(3)}^{x}$

Step 1

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

$y = 2 {(3)}^{- 2}$

Step 2

Solve the equation for $y$ .

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Step 2.1

Remove parentheses.

$y = 2 \cdot 3^{- 2}$

Step 2.2

Remove parentheses.

$y = 2 {(3)}^{- 2}$

Step 2.3

Simplify $2 {(3)}^{- 2}$ .

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Step 2.3.1

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

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

Step 2.3.2

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

$y = 2 (\frac{1}{9})$

Step 2.3.3

Combine $2$ and $\frac{1}{9}$ .

$y = \frac{2}{9}$

Step 3

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

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

Step 4

Solve the equation for $y$ .

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Step 4.1

Remove parentheses.

$y = 2 \cdot 3^{- 1}$

Step 4.2

Remove parentheses.

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

Step 4.3

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

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Step 4.3.1

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

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

Step 4.3.2

Combine $2$ and $\frac{1}{3}$ .

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

Step 5

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

$y = 2 {(3)}^{0}$

Step 6

Solve the equation for $y$ .

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Step 6.1

Remove parentheses.

$y = 2 \cdot 3^{0}$

Step 6.2

Remove parentheses.

$y = 2 {(3)}^{0}$

Step 6.3

Simplify $2 {(3)}^{0}$ .

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Step 6.3.1

Anything raised to $0$ is $1$ .

$y = 2 \cdot 1$

Step 6.3.2

Multiply $2$ by $1$ .

$y = 2$

Step 7

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

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

Step 8

Solve the equation for $y$ .

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Step 8.1

Remove parentheses.

$y = 2 \cdot 3$

Step 8.2

Remove parentheses.

$y = 2 (3)$

Step 8.3

Multiply $2$ by $3$ .

$y = 6$

Step 9

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

$y = 2 {(3)}^{2}$

Step 10

Solve the equation for $y$ .

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Step 10.1

Remove parentheses.

$y = 2 \cdot 3^{2}$

Step 10.2

Remove parentheses.

$y = 2 {(3)}^{2}$

Step 10.3

Simplify $2 {(3)}^{2}$ .

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Step 10.3.1

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

$y = 2 \cdot 9$

Step 10.3.2

Multiply $2$ by $9$ .

$y = 18$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & \frac{2}{9} \\ - 1 & \frac{2}{3} \\ 0 & 2 \\ 1 & 6 \\ 2 & 18 \end{array}$

Step 12