Basic Math Examples

10^{- 4} \div 10^{5}

$10^{- 4} \div 10^{5}$

Step 1

Rewrite the division as a fraction.

\frac{10^{- 4}}{10^{5}}

$\frac{10^{- 4}}{10^{5}}$

Step 2

Move

10^{- 4}

$10^{- 4}$ to the denominator using the negative exponent rule

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

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

\frac{1}{10^{5} \cdot 10^{4}}

$\frac{1}{10^{5} \cdot 10^{4}}$

Step 3

Multiply

10^{5}

$10^{5}$ by

10^{4}

$10^{4}$ by adding the exponents.

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Step 3.1

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

\frac{1}{10^{5 + 4}}

$\frac{1}{10^{5 + 4}}$

Step 3.2

Add

5

$5$ and

4

$4$ .

\frac{1}{10^{9}}

$\frac{1}{10^{9}}$

\frac{1}{10^{9}}

$\frac{1}{10^{9}}$

Step 4

Raise

10

$10$ to the power of

9

$9$ .

\frac{1}{1000000000}

$\frac{1}{1000000000}$

Step 5

The result can be shown in multiple forms.

Exact Form:

\frac{1}{1000000000}

$\frac{1}{1000000000}$

Decimal Form:

1 \cdot 10^{- 9}

$1 \cdot 10^{- 9}$