Algebra Examples

$Y = {(\frac{1}{4})}^{x}$

Step 1

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

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

Step 2

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

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Step 2.1

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

$Y = 4^{2}$

Step 2.2

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

$Y = 16$

Step 3

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

$Y = {(\frac{1}{4})}^{- 1}$

Step 4

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

$Y = 4$

Step 5

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

$Y = {(\frac{1}{4})}^{0}$

Step 6

Simplify ${(\frac{1}{4})}^{0}$ .

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Step 6.1

Apply the product rule to $\frac{1}{4}$ .

$Y = \frac{1^{0}}{4^{0}}$

Step 6.2

Anything raised to $0$ is $1$ .

$Y = \frac{1}{4^{0}}$

Step 6.3

Anything raised to $0$ is $1$ .

$Y = \frac{1}{1}$

Step 6.4

Divide $1$ by $1$ .

$Y = 1$

Step 7

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

$Y = {(\frac{1}{4})}^{1}$

Step 8

Remove parentheses.

$Y = \frac{1}{4}$

Step 9

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

$Y = {(\frac{1}{4})}^{2}$

Step 10

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

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Step 10.1

Apply the product rule to $\frac{1}{4}$ .

$Y = \frac{1^{2}}{4^{2}}$

Step 10.2

One to any power is one.

$Y = \frac{1}{4^{2}}$

Step 10.3

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

$Y = \frac{1}{16}$

Step 11

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

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

Step 12