Basic Math Examples

$(2 \cdot 10^{2}) (2 \cdot 10^{5}) \div 8 \cdot 10^{8}$

Step 1

Multiply $2$ by $2$ .

$4 (10^{2} \cdot 10^{5}) \div 8 \cdot 10^{8}$

Step 2

Multiply $10^{2}$ by $10^{5}$ 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.

$4 \cdot 10^{2 + 5} \div 8 \cdot 10^{8}$

Step 2.2

Add $2$ and $5$ .

$4 \cdot 10^{7} \div 8 \cdot 10^{8}$

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.

$(\frac{4}{8}) (\frac{10^{7}}{1}) \cdot 10^{8}$

Step 3.2

Divide $4$ by $8$ .

$0.5 \frac{10^{7}}{1} \cdot 10^{8}$

Step 3.3

Divide $10^{7}$ by $1$ .

$0.5 \cdot 10^{7} \cdot 10^{8}$

Step 4

Multiply $10^{7}$ by $10^{8}$ by adding the exponents.

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Step 4.1

Move $10^{8}$ .

$0.5 \cdot (10^{8} \cdot 10^{7})$

Step 4.2

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

$0.5 \cdot 10^{8 + 7}$

Step 4.3

Add $8$ and $7$ .

$0.5 \cdot 10^{15}$

Step 5

Move the decimal point in $0.5$ to the right by $1$ place and decrease the power of $10^{15}$ by $1$ .

$5 \cdot 10^{14}$

Step 6

The result can be shown in multiple forms.

Scientific Notation:

$5 \cdot 10^{14}$

Expanded Form:

$500000000000000$