Basic Math Examples

\frac{8 \cdot 10^{15} \cdot 15 \cdot 10^{- 6}}{20 \cdot {(10^{2})}^{5}}

$\frac{8 \cdot 10^{15} \cdot 15 \cdot 10^{- 6}}{20 \cdot {(10^{2})}^{5}}$

Step 1

Multiply

8

$8$ by

15

$15$ .

\frac{120 (10^{15} \cdot 10^{- 6})}{20 \cdot {(10^{2})}^{5}}

$\frac{120 (10^{15} \cdot 10^{- 6})}{20 \cdot {(10^{2})}^{5}}$

Step 2

Multiply

10^{15}

$10^{15}$ by

10^{- 6}

$10^{- 6}$ by adding the exponents.

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Step 2.1

Use the power rule

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

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

\frac{120 \cdot 10^{15 - 6}}{20 \cdot {(10^{2})}^{5}}

$\frac{120 \cdot 10^{15 - 6}}{20 \cdot {(10^{2})}^{5}}$

Step 2.2

Subtract

6

$6$ from

15

$15$ .

\frac{120 \cdot 10^{9}}{20 \cdot {(10^{2})}^{5}}

$\frac{120 \cdot 10^{9}}{20 \cdot {(10^{2})}^{5}}$

\frac{120 \cdot 10^{9}}{20 \cdot {(10^{2})}^{5}}

$\frac{120 \cdot 10^{9}}{20 \cdot {(10^{2})}^{5}}$

Step 3

Cancel the common factor of

120

$120$ and

20

$20$ .

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Step 3.1

Factor

20

$20$ out of

120 \cdot 10^{9}

$120 \cdot 10^{9}$ .

\frac{20 \cdot 6 \cdot 10^{9}}{20 \cdot {(10^{2})}^{5}}

$\frac{20 \cdot 6 \cdot 10^{9}}{20 \cdot {(10^{2})}^{5}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor

20

$20$ out of

20 \cdot {(10^{2})}^{5}

$20 \cdot {(10^{2})}^{5}$ .

\frac{20 \cdot 6 \cdot 10^{9}}{20 ({(10^{2})}^{5})}

$\frac{20 \cdot 6 \cdot 10^{9}}{20 ({(10^{2})}^{5})}$

Step 3.2.2

Cancel the common factor.

$\frac{20 \cdot 6 \cdot 10^{9}}{20 {(10^{2})}^{5}}$

Step 3.2.3

Rewrite the expression.

$\frac{6 \cdot 10^{9}}{{(10^{2})}^{5}}$

Step 4

Simplify the denominator.

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Step 4.1

Multiply the exponents in

${(10^{2})}^{5}$ .

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Step 4.1.1

Apply the power rule and multiply exponents,

${(a^{m})}^{n} = a^{m n}$ .

$\frac{6 \cdot 10^{9}}{10^{2 \cdot 5}}$

Step 4.1.2

Multiply

$2$ by

$5$ .

$\frac{6 \cdot 10^{9}}{10^{10}}$

Step 4.2

Raise

$10$ to the power of

$10$ .

$\frac{6 \cdot 10^{9}}{10000000000}$

Step 5

Divide using scientific notation.

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Step 5.1

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

$(\frac{6}{10000000000}) (\frac{10^{9}}{1})$

Step 5.2

Divide

$6$ by

$10000000000$ .

$0 \frac{10^{9}}{1}$

Step 5.3

Divide

$10^{9}$ by

$1$ .

$0 \cdot 10^{9}$

Step 6

Move the decimal point in

$0$ to the right by

$10$ places and decrease the power of

$10^{9}$ by

$10$ .

$6 \cdot 10^{- 1}$

Step 7

The result can be shown in multiple forms.

Scientific Notation:

$6 \cdot 10^{- 1}$

Expanded Form:

$0.6$