Algebra Examples

$- 2 {(\frac{1}{2})}^{x}$

Step 1

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

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

Step 2

Solve the equation for $y$ .

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Step 2.1

Remove parentheses.

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

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

$y = - 2 \cdot 4$

Step 2.2.3

Multiply $- 2$ by $4$ .

$y = - 8$

Step 3

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

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

Step 4

Solve the equation for $y$ .

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Step 4.1

Remove parentheses.

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

Step 4.2

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

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Step 4.2.1

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

$y = - 2 \cdot 2$

Step 4.2.2

Multiply $- 2$ by $2$ .

$y = - 4$

Step 5

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

$y = - 2 {(\frac{1}{2})}^{0}$

Step 6

Solve the equation for $y$ .

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Step 6.1

Remove parentheses.

$y = - 2 {(\frac{1}{2})}^{0}$

Step 6.2

Simplify $- 2 {(\frac{1}{2})}^{0}$ .

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Step 6.2.1

Simplify the expression.

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Step 6.2.1.1

Apply the product rule to $\frac{1}{2}$ .

$y = - 2 \frac{1^{0}}{2^{0}}$

Step 6.2.1.2

Anything raised to $0$ is $1$ .

$y = - 2 \frac{1}{2^{0}}$

Step 6.2.1.3

Anything raised to $0$ is $1$ .

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

Step 6.2.2

Cancel the common factor of $1$ .

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Step 6.2.2.1

Cancel the common factor.

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

Step 6.2.2.2

Rewrite the expression.

$y = - 2 \cdot 1$

Step 6.2.3

Multiply $- 2$ by $1$ .

$y = - 2$

Step 7

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

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

Step 8

Solve the equation for $y$ .

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Step 8.1

Remove parentheses.

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

Step 8.2

Cancel the common factor of $2$ .

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Step 8.2.1

Factor $2$ out of $- 2$ .

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

Step 8.2.2

Cancel the common factor.

$y = 2 \cdot - 1 \frac{1}{2}$

Step 8.2.3

Rewrite the expression.

$y = - 1$

Step 9

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

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

Step 10

Solve the equation for $y$ .

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Step 10.1

Remove parentheses.

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

Step 10.2

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

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Step 10.2.1

Simplify the expression.

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Step 10.2.1.1

Apply the product rule to $\frac{1}{2}$ .

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

Step 10.2.1.2

One to any power is one.

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

Step 10.2.1.3

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

$y = - 2 (\frac{1}{4})$

Step 10.2.2

Cancel the common factor of $2$ .

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Step 10.2.2.1

Factor $2$ out of $- 2$ .

$y = 2 (- 1) \frac{1}{4}$

Step 10.2.2.2

Factor $2$ out of $4$ .

$y = 2 \cdot - 1 \frac{1}{2 \cdot 2}$

Step 10.2.2.3

Cancel the common factor.

$y = 2 \cdot - 1 \frac{1}{2 \cdot 2}$

Step 10.2.2.4

Rewrite the expression.

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

Step 10.2.3

Rewrite $- 1 (\frac{1}{2})$ as $- (\frac{1}{2})$ .

$y = - \frac{1}{2}$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & - 8 \\ - 1 & - 4 \\ 0 & - 2 \\ 1 & - 1 \\ 2 & - \frac{1}{2} \end{array}$

Step 12