Basic Math Examples

\frac{(6.67 \cdot 10^{- 11}) (5.97 \cdot 10^{24})}{{(6.38 \cdot 10^{6})}^{2}}

$\frac{(6.67 \cdot 10^{- 11}) (5.97 \cdot 10^{24})}{{(6.38 \cdot 10^{6})}^{2}}$

Step 1

Multiply

6.67

$6.67$ by

5.97

$5.97$ .

\frac{39.8199 (10^{- 11} \cdot 10^{24})}{{(6.38 \cdot 10^{6})}^{2}}

$\frac{39.8199 (10^{- 11} \cdot 10^{24})}{{(6.38 \cdot 10^{6})}^{2}}$

Step 2

Multiply

10^{- 11}

$10^{- 11}$ by

10^{24}

$10^{24}$ 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{39.8199 \cdot 10^{- 11 + 24}}{{(6.38 \cdot 10^{6})}^{2}}

$\frac{39.8199 \cdot 10^{- 11 + 24}}{{(6.38 \cdot 10^{6})}^{2}}$

Step 2.2

Add

- 11

$- 11$ and

24

$24$ .

\frac{39.8199 \cdot 10^{13}}{{(6.38 \cdot 10^{6})}^{2}}

$\frac{39.8199 \cdot 10^{13}}{{(6.38 \cdot 10^{6})}^{2}}$

\frac{39.8199 \cdot 10^{13}}{{(6.38 \cdot 10^{6})}^{2}}

$\frac{39.8199 \cdot 10^{13}}{{(6.38 \cdot 10^{6})}^{2}}$

Step 3

Move the decimal point in

39.8199

$39.8199$ to the left by

1

$1$ place and increase the power of

10^{13}

$10^{13}$ by

1

$1$ .

\frac{3.98199 \cdot 10^{14}}{{(6.38 \cdot 10^{6})}^{2}}

$\frac{3.98199 \cdot 10^{14}}{{(6.38 \cdot 10^{6})}^{2}}$

Step 4

Simplify the denominator.

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Step 4.1

Apply the product rule to

6.38 \cdot 10^{6}

$6.38 \cdot 10^{6}$ .

\frac{3.98199 \cdot 10^{14}}{{6.38}^{2} \cdot {(10^{6})}^{2}}

$\frac{3.98199 \cdot 10^{14}}{{6.38}^{2} \cdot {(10^{6})}^{2}}$

Step 4.2

Raise

6.38

$6.38$ to the power of

2

$2$ .

\frac{3.98199 \cdot 10^{14}}{40.7044 \cdot {(10^{6})}^{2}}

$\frac{3.98199 \cdot 10^{14}}{40.7044 \cdot {(10^{6})}^{2}}$

Step 4.3

Multiply the exponents in

{(10^{6})}^{2}

${(10^{6})}^{2}$ .

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Step 4.3.1

Apply the power rule and multiply exponents,

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

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

\frac{3.98199 \cdot 10^{14}}{40.7044 \cdot 10^{6 \cdot 2}}

$\frac{3.98199 \cdot 10^{14}}{40.7044 \cdot 10^{6 \cdot 2}}$

Step 4.3.2

Multiply

6

$6$ by

2

$2$ .

\frac{3.98199 \cdot 10^{14}}{40.7044 \cdot 10^{12}}

$\frac{3.98199 \cdot 10^{14}}{40.7044 \cdot 10^{12}}$

\frac{3.98199 \cdot 10^{14}}{40.7044 \cdot 10^{12}}

$\frac{3.98199 \cdot 10^{14}}{40.7044 \cdot 10^{12}}$

Step 4.4

Raise

10

$10$ to the power of

12

$12$ .

\frac{3.98199 \cdot 10^{14}}{40.7044 \cdot 1000000000000}

$\frac{3.98199 \cdot 10^{14}}{40.7044 \cdot 1000000000000}$

\frac{3.98199 \cdot 10^{14}}{40.7044 \cdot 1000000000000}

$\frac{3.98199 \cdot 10^{14}}{40.7044 \cdot 1000000000000}$

Step 5

Multiply

40.7044

$40.7044$ by

1000000000000

$1000000000000$ .

\frac{3.98199 \cdot 10^{14}}{40704400000000}

$\frac{3.98199 \cdot 10^{14}}{40704400000000}$

Step 6

Divide using scientific notation.

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Step 6.1

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

(\frac{3.98199}{40704400000000}) (\frac{10^{14}}{1})

$(\frac{3.98199}{40704400000000}) (\frac{10^{14}}{1})$

Step 6.2

Divide

3.98199

$3.98199$ by

40704400000000

$40704400000000$ .

0 \frac{10^{14}}{1}

$0 \frac{10^{14}}{1}$

Step 6.3

Divide

10^{14}

$10^{14}$ by

1

$1$ .

0 \cdot 10^{14}

$0 \cdot 10^{14}$

0 \cdot 10^{14}

$0 \cdot 10^{14}$

Step 7

Move the decimal point in

0

$0$ to the right by

14

$14$ places and decrease the power of

10^{14}

$10^{14}$ by

14

$14$ .

9.78270162 \cdot 10^{0}

$9.78270162 \cdot 10^{0}$

Step 8

Convert

9.78270162 \cdot 10^{0}

$9.78270162 \cdot 10^{0}$ from scientific notation.

9.78270162

$9.78270162$