Algebra Examples

$y = - 2 {(\frac{1}{4})}^{x - 3}$

Step 1

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

$y = - 2 {(\frac{1}{4})}^{(- 2) - 3}$

Step 2

Solve the equation for $y$ .

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Step 2.1

Remove parentheses.

$y = - 2 {(\frac{1}{4})}^{- 2 - 3}$

Step 2.2

Remove parentheses.

$y = - 2 {(\frac{1}{4})}^{(- 2) - 3}$

Step 2.3

Simplify $- 2 {(\frac{1}{4})}^{(- 2) - 3}$ .

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Step 2.3.1

Subtract $3$ from $- 2$ .

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

Step 2.3.2

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

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

Step 2.3.3

Raise $4$ to the power of $5$ .

$y = - 2 \cdot 1024$

Step 2.3.4

Multiply $- 2$ by $1024$ .

$y = - 2048$

Step 3

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

$y = - 2 {(\frac{1}{4})}^{(- 1) - 3}$

Step 4

Solve the equation for $y$ .

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Step 4.1

Remove parentheses.

$y = - 2 {(\frac{1}{4})}^{- 1 - 3}$

Step 4.2

Remove parentheses.

$y = - 2 {(\frac{1}{4})}^{(- 1) - 3}$

Step 4.3

Simplify $- 2 {(\frac{1}{4})}^{(- 1) - 3}$ .

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Step 4.3.1

Subtract $3$ from $- 1$ .

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

Step 4.3.2

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

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

Step 4.3.3

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

$y = - 2 \cdot 256$

Step 4.3.4

Multiply $- 2$ by $256$ .

$y = - 512$

Step 5

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

$y = - 2 {(\frac{1}{4})}^{(0) - 3}$

Step 6

Solve the equation for $y$ .

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Step 6.1

Remove parentheses.

$y = - 2 {(\frac{1}{4})}^{0 - 3}$

Step 6.2

Remove parentheses.

$y = - 2 {(\frac{1}{4})}^{(0) - 3}$

Step 6.3

Simplify $- 2 {(\frac{1}{4})}^{(0) - 3}$ .

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Step 6.3.1

Subtract $3$ from $0$ .

$y = - 2 {(\frac{1}{4})}^{- 3}$

Step 6.3.2

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

$y = - 2 \cdot 4^{3}$

Step 6.3.3

Raise $4$ to the power of $3$ .

$y = - 2 \cdot 64$

Step 6.3.4

Multiply $- 2$ by $64$ .

$y = - 128$

Step 7

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

$y = - 2 {(\frac{1}{4})}^{(1) - 3}$

Step 8

Solve the equation for $y$ .

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Step 8.1

Remove parentheses.

$y = - 2 {(\frac{1}{4})}^{1 - 3}$

Step 8.2

Remove parentheses.

$y = - 2 {(\frac{1}{4})}^{(1) - 3}$

Step 8.3

Simplify $- 2 {(\frac{1}{4})}^{(1) - 3}$ .

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Step 8.3.1

Subtract $3$ from $1$ .

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

Step 8.3.2

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

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

Step 8.3.3

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

$y = - 2 \cdot 16$

Step 8.3.4

Multiply $- 2$ by $16$ .

$y = - 32$

Step 9

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

$y = - 2 {(\frac{1}{4})}^{(2) - 3}$

Step 10

Solve the equation for $y$ .

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Step 10.1

Remove parentheses.

$y = - 2 {(\frac{1}{4})}^{2 - 3}$

Step 10.2

Remove parentheses.

$y = - 2 {(\frac{1}{4})}^{(2) - 3}$

Step 10.3

Simplify $- 2 {(\frac{1}{4})}^{(2) - 3}$ .

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Step 10.3.1

Subtract $3$ from $2$ .

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

Step 10.3.2

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

$y = - 2 \cdot 4$

Step 10.3.3

Multiply $- 2$ by $4$ .

$y = - 8$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & - 2048 \\ - 1 & - 512 \\ 0 & - 128 \\ 1 & - 32 \\ 2 & - 8 \end{array}$

Step 12