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

Multiply $2$ by $2^{2}$ by adding the exponents.

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Step 2.2.2.1

Multiply $2$ by $2^{2}$ .

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Step 2.2.2.1.1

Raise $2$ to the power of $1$ .

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

Step 2.2.2.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = 2^{1 + 2}$

Step 2.2.2.2

Add $1$ and $2$ .

$y = 2^{3}$

Step 2.2.3

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

$y = 8$

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

Cancel the common factor.

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

Step 8.2.2

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 $4$ .

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

Step 10.2.2.2

Cancel the common factor.

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

Step 10.2.2.3

Rewrite the expression.

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

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