Basic Math Examples

10^{- 2} - 10^{- 3}

$10^{- 2} - 10^{- 3}$

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}}

$b^{- n} = \frac{1}{b^{n}}$ .

\frac{1}{10^{2}} - 10^{- 3}

$\frac{1}{10^{2}} - 10^{- 3}$

Step 1.2

Raise

10

$10$ to the power of

2

$2$ .

\frac{1}{100} - 10^{- 3}

$\frac{1}{100} - 10^{- 3}$

Step 1.3

Rewrite the expression using the negative exponent rule

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ .

\frac{1}{100} - \frac{1}{10^{3}}

$\frac{1}{100} - \frac{1}{10^{3}}$

Step 1.4

Raise

10

$10$ to the power of

3

$3$ .

\frac{1}{100} - \frac{1}{1000}

$\frac{1}{100} - \frac{1}{1000}$

\frac{1}{100} - \frac{1}{1000}

$\frac{1}{100} - \frac{1}{1000}$

Step 2

To write

\frac{1}{100}

$\frac{1}{100}$ as a fraction with a common denominator, multiply by

\frac{10}{10}

$\frac{10}{10}$ .

\frac{1}{100} \cdot \frac{10}{10} - \frac{1}{1000}

$\frac{1}{100} \cdot \frac{10}{10} - \frac{1}{1000}$

Step 3

Write each expression with a common denominator of

1000

$1000$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 3.1

Multiply

\frac{1}{100}

$\frac{1}{100}$ by

\frac{10}{10}

$\frac{10}{10}$ .

\frac{10}{100 \cdot 10} - \frac{1}{1000}

$\frac{10}{100 \cdot 10} - \frac{1}{1000}$

Step 3.2

Multiply

100

$100$ by

10

$10$ .

\frac{10}{1000} - \frac{1}{1000}

$\frac{10}{1000} - \frac{1}{1000}$

\frac{10}{1000} - \frac{1}{1000}

$\frac{10}{1000} - \frac{1}{1000}$

Step 4

Combine the numerators over the common denominator.

\frac{10 - 1}{1000}

$\frac{10 - 1}{1000}$

Step 5

Subtract

1

$1$ from

10

$10$ .

\frac{9}{1000}

$\frac{9}{1000}$

Step 6

The result can be shown in multiple forms.

Exact Form:

\frac{9}{1000}

$\frac{9}{1000}$

Decimal Form:

0.009

$0.009$