Algebra Examples

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

Step 1

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

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

Step 2

Simplify $2 \cdot 2^{- 2}$ .

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Step 2.1

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

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Step 2.1.1

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

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Step 2.1.1.1

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

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

Step 2.1.1.2

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

$y = 2^{1 - 2}$

Step 2.1.2

Subtract $2$ from $1$ .

$y = 2^{- 1}$

Step 2.2

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

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

Step 3

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

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

Step 4

Simplify $2 \cdot 2^{- 1}$ .

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Step 4.1

Multiply $2$ by $2^{- 1}$ by adding the exponents.

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Step 4.1.1

Multiply $2$ by $2^{- 1}$ .

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Step 4.1.1.1

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

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

Step 4.1.1.2

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

$y = 2^{1 - 1}$

Step 4.1.2

Subtract $1$ from $1$ .

$y = 2^{0}$

Step 4.2

Simplify $2^{0}$ .

$y = 1$

Step 5

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

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

Step 6

Simplify $2 \cdot 2^{0}$ .

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Step 6.1

Multiply $2$ by $2^{0}$ by adding the exponents.

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Step 6.1.1

Multiply $2$ by $2^{0}$ .

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Step 6.1.1.1

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

$y = 2^{1} \cdot 2^{0}$

Step 6.1.1.2

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

$y = 2^{1 + 0}$

Step 6.1.2

Add $1$ and $0$ .

$y = 2^{1}$

Step 6.2

Simplify $2^{1}$ .

$y = 2$

Step 7

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

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

Step 8

Simplify $2 \cdot 2^{1}$ .

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Step 8.1

Evaluate the exponent.

$y = 2 \cdot 2$

Step 8.2

Multiply $2$ by $2$ .

$y = 4$

Step 9

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

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

Step 10

Simplify $2 \cdot 2^{2}$ .

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Step 10.1

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

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Step 10.1.1

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

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Step 10.1.1.1

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

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

Step 10.1.1.2

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

$y = 2^{1 + 2}$

Step 10.1.2

Add $1$ and $2$ .

$y = 2^{3}$

Step 10.2

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

$y = 8$

Step 11

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

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

Step 12