Graph Using a Table of Values (1/4)^x

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

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

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

Solve the equation for $y$ .

Remove parentheses.

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

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

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

$y = 4^{2}$

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

$y = 16$

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

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

Solve the equation for $y$ .

Remove parentheses.

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

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

$y = 4$

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

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

Solve the equation for $y$ .

Remove parentheses.

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

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

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

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

Anything raised to $0$ is $1$ .

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

Anything raised to $0$ is $1$ .

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

Divide $1$ by $1$ .

$y = 1$

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

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

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

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

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

Solve the equation for $y$ .

Remove parentheses.

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

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

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

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

One to any power is one.

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

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

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

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

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

Graph Using a Table of Values (1/4)^x

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