Evaluate Using the Given Value y^-3-y^-2 , y=2

$y^{- 3} - y^{- 2}$ , $y = 2$

Step 1

Replace the variable $y$ with $2$ in the expression.

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

Step 2

Simplify each term.

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

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

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

$\frac{1}{8} - {(2)}^{- 2}$

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

$\frac{1}{8} - \frac{1}{2^{2}}$

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

$\frac{1}{8} - \frac{1}{4}$

Step 3

To write $- \frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{8} - \frac{1}{4} \cdot \frac{2}{2}$

Step 4

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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

$\frac{1}{8} - \frac{2}{4 \cdot 2}$

Multiply $4$ by $2$ .

$\frac{1}{8} - \frac{2}{8}$

Step 5

Combine the numerators over the common denominator.

$\frac{1 - 2}{8}$

Step 6

Subtract $2$ from $1$ .

$\frac{- 1}{8}$

Step 7

Move the negative in front of the fraction.

$- \frac{1}{8}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{8}$

Decimal Form:

$- 0.125$