Algebra Examples

$f (x) = - \frac{5}{2} {(2)}^{x}$

Step 1

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

$y = - \frac{5}{2} \cdot {(2)}^{- 2}$

Step 2

Solve the equation for $y$ .

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Step 2.1

Remove parentheses.

$y = - \frac{5}{2} \cdot 2^{- 2}$

Step 2.2

Remove parentheses.

$y = - \frac{5}{2} \cdot {(2)}^{- 2}$

Step 2.3

Simplify $- \frac{5}{2} \cdot {(2)}^{- 2}$ .

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Step 2.3.1

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

$y = - \frac{5}{2} \cdot \frac{1}{2^{2}}$

Step 2.3.2

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

$y = - \frac{5}{2} \cdot \frac{1}{4}$

Step 2.3.3

Multiply $- \frac{5}{2} \cdot \frac{1}{4}$ .

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Step 2.3.3.1

Multiply $\frac{1}{4}$ by $\frac{5}{2}$ .

$y = - \frac{5}{4 \cdot 2}$

Step 2.3.3.2

Multiply $4$ by $2$ .

$y = - \frac{5}{8}$

Step 3

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

$y = - \frac{5}{2} \cdot {(2)}^{- 1}$

Step 4

Solve the equation for $y$ .

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Step 4.1

Remove parentheses.

$y = - \frac{5}{2} \cdot 2^{- 1}$

Step 4.2

Remove parentheses.

$y = - \frac{5}{2} \cdot {(2)}^{- 1}$

Step 4.3

Simplify $- \frac{5}{2} \cdot {(2)}^{- 1}$ .

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Step 4.3.1

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

$y = - \frac{5}{2} \cdot \frac{1}{2}$

Step 4.3.2

Multiply $- \frac{5}{2} \cdot \frac{1}{2}$ .

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Step 4.3.2.1

Multiply $\frac{1}{2}$ by $\frac{5}{2}$ .

$y = - \frac{5}{2 \cdot 2}$

Step 4.3.2.2

Multiply $2$ by $2$ .

$y = - \frac{5}{4}$

Step 5

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

$y = - \frac{5}{2} \cdot {(2)}^{0}$

Step 6

Solve the equation for $y$ .

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Step 6.1

Remove parentheses.

$y = - \frac{5}{2} \cdot 2^{0}$

Step 6.2

Remove parentheses.

$y = - \frac{5}{2} \cdot {(2)}^{0}$

Step 6.3

Simplify $- \frac{5}{2} \cdot {(2)}^{0}$ .

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Step 6.3.1

Anything raised to $0$ is $1$ .

$y = - \frac{5}{2} \cdot 1$

Step 6.3.2

Multiply $- 1$ by $1$ .

$y = - \frac{5}{2}$

Step 7

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

$y = - \frac{5}{2} \cdot {(2)}^{1}$

Step 8

Solve the equation for $y$ .

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Step 8.1

Remove parentheses.

$y = - \frac{5}{2} \cdot 2$

Step 8.2

Remove parentheses.

$y = - \frac{5}{2} \cdot 2$

Step 8.3

Cancel the common factor of $2$ .

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Step 8.3.1

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$y = \frac{- 5}{2} \cdot 2$

Step 8.3.2

Cancel the common factor.

$y = \frac{- 5}{2} \cdot 2$

Step 8.3.3

Rewrite the expression.

$y = - 5$

Step 9

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

$y = - \frac{5}{2} \cdot {(2)}^{2}$

Step 10

Solve the equation for $y$ .

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Step 10.1

Remove parentheses.

$y = - \frac{5}{2} \cdot 2^{2}$

Step 10.2

Remove parentheses.

$y = - \frac{5}{2} \cdot {(2)}^{2}$

Step 10.3

Simplify $- \frac{5}{2} \cdot {(2)}^{2}$ .

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Step 10.3.1

Cancel the common factor of $2$ .

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Step 10.3.1.1

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$y = \frac{- 5}{2} \cdot {(2)}^{2}$

Step 10.3.1.2

Factor $2$ out of ${(2)}^{2}$ .

$y = \frac{- 5}{2} \cdot (2 \cdot 2)$

Step 10.3.1.3

Cancel the common factor.

$y = \frac{- 5}{2} \cdot (2 \cdot 2)$

Step 10.3.1.4

Rewrite the expression.

$y = - 5 \cdot 2$

Step 10.3.2

Multiply $- 5$ by $2$ .

$y = - 10$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & - \frac{5}{8} \\ - 1 & - \frac{5}{4} \\ 0 & - \frac{5}{2} \\ 1 & - 5 \\ 2 & - 10 \end{array}$

Step 12