Algebra Examples

$f (x) = \frac{5}{4} {(2)}^{x}$

Step 1

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

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

Step 2

Solve the equation for $y$ .

Tap for more steps...

Step 2.1

Remove parentheses.

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

Step 2.2

Remove parentheses.

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

Step 2.3

Simplify $\frac{5}{4} \cdot {(2)}^{- 2}$ .

Tap for more steps...

Step 2.3.1

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

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

Step 2.3.2

Combine fractions.

Tap for more steps...

Step 2.3.2.1

Combine.

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

Step 2.3.2.2

Multiply $5$ by $1$ .

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

Step 2.3.3

Simplify the denominator.

Tap for more steps...

Step 2.3.3.1

Rewrite $4$ as $2^{2}$ .

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

Step 2.3.3.2

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

$y = \frac{5}{2^{2 + 2}}$

Step 2.3.3.3

Add $2$ and $2$ .

$y = \frac{5}{2^{4}}$

Step 2.3.4

Raise $2$ to the power of $4$ .

$y = \frac{5}{16}$

Step 3

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

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

Step 4

Solve the equation for $y$ .

Tap for more steps...

Step 4.1

Remove parentheses.

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

Step 4.2

Remove parentheses.

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

Step 4.3

Simplify $\frac{5}{4} \cdot {(2)}^{- 1}$ .

Tap for more steps...

Step 4.3.1

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

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

Step 4.3.2

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

Tap for more steps...

Step 4.3.2.1

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

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

Step 4.3.2.2

Multiply $4$ by $2$ .

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

Step 5

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

$y = \frac{5}{4} \cdot {(2)}^{0}$

Step 6

Solve the equation for $y$ .

Tap for more steps...

Step 6.1

Remove parentheses.

$y = \frac{5}{4} \cdot 2^{0}$

Step 6.2

Remove parentheses.

$y = \frac{5}{4} \cdot {(2)}^{0}$

Step 6.3

Simplify $\frac{5}{4} \cdot {(2)}^{0}$ .

Tap for more steps...

Step 6.3.1

Anything raised to $0$ is $1$ .

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

Step 6.3.2

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

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

Step 7

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

$y = \frac{5}{4} \cdot {(2)}^{1}$

Step 8

Solve the equation for $y$ .

Tap for more steps...

Step 8.1

Remove parentheses.

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

Step 8.2

Remove parentheses.

$y = \frac{5}{4} \cdot (2)$

Step 8.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 8.3.1

Factor $2$ out of $4$ .

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

Step 8.3.2

Cancel the common factor.

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

Step 8.3.3

Rewrite the expression.

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

Step 9

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

$y = \frac{5}{4} \cdot {(2)}^{2}$

Step 10

Solve the equation for $y$ .

Tap for more steps...

Step 10.1

Remove parentheses.

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

Step 10.2

Remove parentheses.

$y = \frac{5}{4} \cdot {(2)}^{2}$

Step 10.3

Simplify $\frac{5}{4} \cdot {(2)}^{2}$ .

Tap for more steps...

Step 10.3.1

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

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

Step 10.3.2

Cancel the common factor of $4$ .

Tap for more steps...

Step 10.3.2.1

Cancel the common factor.

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

Step 10.3.2.2

Rewrite the expression.

$y = 5$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & \frac{5}{16} \\ - 1 & \frac{5}{8} \\ 0 & \frac{5}{4} \\ 1 & \frac{5}{2} \\ 2 & 5 \end{array}$

Step 12