Basic Math Examples

$\frac{2 \cdot 10^{5} \cdot 6 \cdot 10^{2}}{4 \cdot 10^{4}}$

Step 1

Multiply $2$ by $6$ .

$\frac{12 (10^{5} \cdot 10^{2})}{4 \cdot 10^{4}}$

Step 2

Multiply $10^{5}$ by $10^{2}$ by adding the exponents.

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Step 2.1

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

$\frac{12 \cdot 10^{5 + 2}}{4 \cdot 10^{4}}$

Step 2.2

Add $5$ and $2$ .

$\frac{12 \cdot 10^{7}}{4 \cdot 10^{4}}$

Step 3

Divide using scientific notation.

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Step 3.1

Group coefficients together and exponents together to divide numbers in scientific notation.

$(\frac{12}{4}) (\frac{10^{7}}{10^{4}})$

Step 3.2

Divide $12$ by $4$ .

$3 \frac{10^{7}}{10^{4}}$

Step 3.3

Subtract the exponent from the denominator from the exponent of the numerator for the same base

$3 \cdot 10^{7 + 4 \cdot - 1}$

Step 3.4

Multiply $4$ by $- 1$ .

$3 \cdot 10^{7 - 4}$

Step 3.5

Subtract $4$ from $7$ .

$3 \cdot 10^{3}$

Step 4

The result can be shown in multiple forms.

Scientific Notation:

$3 \cdot 10^{3}$

Expanded Form:

$3000$