Basic Math Examples

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

Step 1

Multiply $6.67$ by $5.97$ .

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

Step 2

Multiply $10^{- 11}$ by $10^{24}$ 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.

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

Step 2.2

Add $- 11$ and $24$ .

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

Step 3

Move the decimal point in $39.8199$ to the left by $1$ place and increase the power of $10^{13}$ by $1$ .

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

Step 4

Simplify the denominator.

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Step 4.1

Apply the product rule to $6.38 \cdot 10^{6}$ .

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

Step 4.2

Raise $6.38$ to the power of $2$ .

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

Step 4.3

Multiply the exponents in ${(10^{6})}^{2}$ .

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Step 4.3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 4.3.2

Multiply $6$ by $2$ .

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

Step 4.4

Raise $10$ to the power of $12$ .

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

Step 5

Multiply $40.7044$ by $1000000000000$ .

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

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.

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

Step 6.2

Divide $3.98199$ by $40704400000000$ .

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

Step 6.3

Divide $10^{14}$ by $1$ .

$0 \cdot 10^{14}$

Step 7

Move the decimal point in $0$ to the right by $14$ places and decrease the power of $10^{14}$ by $14$ .

$9.78270162 \cdot 10^{0}$

Step 8

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

$9.78270162$