Algebra Examples

$y = x^{- 3}$

Step 1

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

$y = {(- 2)}^{- 3}$

Step 2

Simplify ${(- 2)}^{- 3}$ .

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Step 2.1

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

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

Step 2.2

Raise $- 2$ to the power of $3$ .

$y = \frac{1}{- 8}$

Step 2.3

Move the negative in front of the fraction.

$y = - \frac{1}{8}$

Step 3

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

$y = {(- 1)}^{- 3}$

Step 4

Simplify ${(- 1)}^{- 3}$ .

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Step 4.1

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

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

Step 4.2

Raise $- 1$ to the power of $3$ .

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

Step 4.3

Divide $1$ by $- 1$ .

$y = - 1$

Step 5

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

$y = {(1)}^{- 3}$

Step 6

Solve the equation for $y$ .

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Step 6.1

Remove parentheses.

$y = 1^{- 3}$

Step 6.2

Remove parentheses.

$y = {(1)}^{- 3}$

Step 6.3

One to any power is one.

$y = 1$

Step 7

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

$y = {(2)}^{- 3}$

Step 8

Solve the equation for $y$ .

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Step 8.1

Remove parentheses.

$y = 2^{- 3}$

Step 8.2

Remove parentheses.

$y = {(2)}^{- 3}$

Step 8.3

Simplify ${(2)}^{- 3}$ .

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Step 8.3.1

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

$y = \frac{1}{2^{3}}$

Step 8.3.2

Raise $2$ to the power of $3$ .

$y = \frac{1}{8}$

Step 9

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

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

Step 10