Algebra Examples

$8^{- 1} - 3^{- 1}$

Step 1

Simplify each term.

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Step 1.1

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

$\frac{1}{8} - 3^{- 1}$

Step 1.2

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

$\frac{1}{8} - \frac{1}{3}$

Step 2

To write $\frac{1}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{8} \cdot \frac{3}{3} - \frac{1}{3}$

Step 3

To write $- \frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{1}{8} \cdot \frac{3}{3} - \frac{1}{3} \cdot \frac{8}{8}$

Step 4

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{1}{8}$ by $\frac{3}{3}$ .

$\frac{3}{8 \cdot 3} - \frac{1}{3} \cdot \frac{8}{8}$

Step 4.2

Multiply $8$ by $3$ .

$\frac{3}{24} - \frac{1}{3} \cdot \frac{8}{8}$

Step 4.3

Multiply $\frac{1}{3}$ by $\frac{8}{8}$ .

$\frac{3}{24} - \frac{8}{3 \cdot 8}$

Step 4.4

Multiply $3$ by $8$ .

$\frac{3}{24} - \frac{8}{24}$

Step 5

Combine the numerators over the common denominator.

$\frac{3 - 8}{24}$

Step 6

Subtract $8$ from $3$ .

$\frac{- 5}{24}$

Step 7

Move the negative in front of the fraction.

$- \frac{5}{24}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- \frac{5}{24}$

Decimal Form:

$- 0.208\overline{3}$