Simplify 5^-1-2^-3

$5^{- 1} - 2^{- 3}$

Step 1

Simplify each term.

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

$\frac{1}{5} - 2^{- 3}$

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

$\frac{1}{5} - \frac{1}{2^{3}}$

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

$\frac{1}{5} - \frac{1}{8}$

Step 2

To write $\frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{1}{5} \cdot \frac{8}{8} - \frac{1}{8}$

Step 3

To write $- \frac{1}{8}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{1}{5} \cdot \frac{8}{8} - \frac{1}{8} \cdot \frac{5}{5}$

Step 4

Write each expression with a common denominator of $40$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{5}$ by $\frac{8}{8}$ .

$\frac{8}{5 \cdot 8} - \frac{1}{8} \cdot \frac{5}{5}$

Multiply $5$ by $8$ .

$\frac{8}{40} - \frac{1}{8} \cdot \frac{5}{5}$

Multiply $\frac{1}{8}$ by $\frac{5}{5}$ .

$\frac{8}{40} - \frac{5}{8 \cdot 5}$

Multiply $8$ by $5$ .

$\frac{8}{40} - \frac{5}{40}$

Step 5

Combine the numerators over the common denominator.

$\frac{8 - 5}{40}$

Step 6

Subtract $5$ from $8$ .

$\frac{3}{40}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{40}$

Decimal Form:

$0.075$