Basic Math Examples

$\frac{10^{8} \cdot 10^{- 5}}{10^{6} \cdot 10^{3}} \cdot \frac{10^{2} \cdot 10^{- 7}}{10^{3} \cdot 10^{- 5}}$

Step 1

Multiply $10^{8}$ by $10^{- 5}$ by adding the exponents.

Tap for more steps...

Step 1.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{10^{8 - 5}}{10^{6} \cdot 10^{3}} \cdot \frac{10^{2} \cdot 10^{- 7}}{10^{3} \cdot 10^{- 5}}$

Step 1.2

Subtract $5$ from $8$ .

$\frac{10^{3}}{10^{6} \cdot 10^{3}} \cdot \frac{10^{2} \cdot 10^{- 7}}{10^{3} \cdot 10^{- 5}}$

Step 2

Multiply $10^{6}$ by $10^{3}$ by adding the exponents.

Tap for more steps...

Step 2.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{10^{3}}{10^{6 + 3}} \cdot \frac{10^{2} \cdot 10^{- 7}}{10^{3} \cdot 10^{- 5}}$

Step 2.2

Add $6$ and $3$ .

$\frac{10^{3}}{10^{9}} \cdot \frac{10^{2} \cdot 10^{- 7}}{10^{3} \cdot 10^{- 5}}$

Step 3

Multiply $10^{2}$ by $10^{- 7}$ by adding the exponents.

Tap for more steps...

Step 3.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{10^{3}}{10^{9}} \cdot \frac{10^{2 - 7}}{10^{3} \cdot 10^{- 5}}$

Step 3.2

Subtract $7$ from $2$ .

$\frac{10^{3}}{10^{9}} \cdot \frac{10^{- 5}}{10^{3} \cdot 10^{- 5}}$

Step 4

Multiply $10^{3}$ by $10^{- 5}$ by adding the exponents.

Tap for more steps...

Step 4.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{10^{3}}{10^{9}} \cdot \frac{10^{- 5}}{10^{3 - 5}}$

Step 4.2

Subtract $5$ from $3$ .

$\frac{10^{3}}{10^{9}} \cdot \frac{10^{- 5}}{10^{- 2}}$

Step 5

Combine.

$\frac{10^{3} \cdot 10^{- 5}}{10^{9} \cdot 10^{- 2}}$

Step 6

Multiply $10^{3}$ by $10^{- 5}$ by adding the exponents.

Tap for more steps...

Step 6.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{10^{3 - 5}}{10^{9} \cdot 10^{- 2}}$

Step 6.2

Subtract $5$ from $3$ .

$\frac{10^{- 2}}{10^{9} \cdot 10^{- 2}}$

Step 7

Multiply $10^{9}$ by $10^{- 2}$ by adding the exponents.

Tap for more steps...

Step 7.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{10^{- 2}}{10^{9 - 2}}$

Step 7.2

Subtract $2$ from $9$ .

$\frac{10^{- 2}}{10^{7}}$

Step 8

Move $10^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{10^{7} \cdot 10^{2}}$

Step 9

Multiply $10^{7}$ by $10^{2}$ by adding the exponents.

Tap for more steps...

Step 9.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1}{10^{7 + 2}}$

Step 9.2

Add $7$ and $2$ .

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

Step 10

Raise $10$ to the power of $9$ .

$\frac{1}{1000000000}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{1000000000}$

Decimal Form:

$1 \cdot 10^{- 9}$