Basic Math Examples

$F = 6.674 \cdot 10^{- 11} \cdot \frac{7.348 \cdot 10^{22} \cdot 5.9722 \cdot 10^{24}}{3.84 \cdot 10^{8}}$

Step 1

Remove parentheses.

$F = 6.674 \cdot 10^{- 11} \cdot \frac{7.348 \cdot 10^{22} \cdot 5.9722 \cdot 10^{24}}{3.84 \cdot 10^{8}}$

Step 2

Simplify $6.674 \cdot 10^{- 11} \cdot \frac{7.348 \cdot 10^{22} \cdot 5.9722 \cdot 10^{24}}{3.84 \cdot 10^{8}}$ .

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Step 2.1

Multiply $7.348$ by $5.9722$ .

$F = 6.674 \cdot 10^{- 11} \cdot \frac{43.8837256 (10^{22} \cdot 10^{24})}{3.84 \cdot 10^{8}}$

Step 2.2

Multiply $10^{22}$ by $10^{24}$ by adding the exponents.

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Step 2.2.1

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

$F = 6.674 \cdot 10^{- 11} \cdot \frac{43.8837256 \cdot 10^{22 + 24}}{3.84 \cdot 10^{8}}$

Step 2.2.2

Add $22$ and $24$ .

$F = 6.674 \cdot 10^{- 11} \cdot \frac{43.8837256 \cdot 10^{46}}{3.84 \cdot 10^{8}}$

Step 2.3

Divide using scientific notation.

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Step 2.3.1

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

$F = 6.674 \cdot 10^{- 11} \cdot ((\frac{43.8837256}{3.84}) (\frac{10^{46}}{10^{8}}))$

Step 2.3.2

Divide $43.8837256$ by $3.84$ .

$F = 6.674 \cdot 10^{- 11} \cdot (11.42805354 \frac{10^{46}}{10^{8}})$

Step 2.3.3

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

$F = 6.674 \cdot 10^{- 11} \cdot (11.42805354 \cdot 10^{46 + 8 \cdot - 1})$

Step 2.3.4

Multiply $8$ by $- 1$ .

$F = 6.674 \cdot 10^{- 11} \cdot (11.42805354 \cdot 10^{46 - 8})$

Step 2.3.5

Subtract $8$ from $46$ .

$F = 6.674 \cdot 10^{- 11} \cdot 11.42805354 \cdot 10^{38}$

Step 2.4

Multiply $6.674$ by $11.42805354$ .

$F = 76.27082933 (10^{- 11} \cdot 10^{38})$

Step 2.5

Multiply $10^{- 11}$ by $10^{38}$ by adding the exponents.

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Step 2.5.1

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

$F = 76.27082933 \cdot 10^{- 11 + 38}$

Step 2.5.2

Add $- 11$ and $38$ .

$F = 76.27082933 \cdot 10^{27}$

Step 2.6

Move the decimal point in $76.27082933$ to the left by $1$ place and increase the power of $10^{27}$ by $1$ .

$F = 7.62708293 \cdot 10^{28}$