Basic Math Examples

$\frac{10^{- 3}}{{6.63}^{- 34} \cdot 3 \cdot \frac{10^{8}}{633 \cdot 10^{- 9}}}$

Step 1

Divide using scientific notation.

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Step 1.1

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

$\frac{10^{- 3}}{{6.63}^{- 34} \cdot 3 \cdot ((\frac{1}{633}) (\frac{10^{8}}{10^{- 9}}))}$

Step 1.2

Divide $1$ by $633$ .

$\frac{10^{- 3}}{{6.63}^{- 34} \cdot 3 \cdot (0.00157977 \frac{10^{8}}{10^{- 9}})}$

Step 1.3

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

$\frac{10^{- 3}}{{6.63}^{- 34} \cdot 3 \cdot (0.00157977 \cdot 10^{8 - 9 \cdot - 1})}$

Step 1.4

Multiply $- 9$ by $- 1$ .

$\frac{10^{- 3}}{{6.63}^{- 34} \cdot 3 \cdot (0.00157977 \cdot 10^{8 + 9})}$

Step 1.5

Add $8$ and $9$ .

$\frac{10^{- 3}}{{6.63}^{- 34} \cdot 3 \cdot 0.00157977 \cdot 10^{17}}$

Step 2

Move $10^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{6.63}^{- 34} \cdot 3 \cdot 0.00157977 \cdot 10^{17} \cdot 10^{3}}$

Step 3

Multiply $10^{17}$ by $10^{3}$ by adding the exponents.

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Step 3.1

Move $10^{3}$ .

$\frac{1}{{6.63}^{- 34} \cdot 3 \cdot (0.00157977 \cdot (10^{3} \cdot 10^{17}))}$

Step 3.2

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

$\frac{1}{{6.63}^{- 34} \cdot 3 \cdot (0.00157977 \cdot 10^{3 + 17})}$

Step 3.3

Add $3$ and $17$ .

$\frac{1}{{6.63}^{- 34} \cdot 3 \cdot 0.00157977 \cdot 10^{20}}$

Step 4

Move ${6.63}^{- 34}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{{6.63}^{34}}{3 \cdot 0.00157977 \cdot 10^{20}}$

Step 5

Raise $6.63$ to the power of $34$ .

$\frac{8540041197781060000000000000}{3 \cdot 0.00157977 \cdot 10^{20}}$

Step 6

Multiply $3$ by $0.00157977$ .

$\frac{8540041197781060000000000000}{0.00473933 \cdot 10^{20}}$

Step 7

Move the decimal point in $0.00473933$ to the right by $3$ places and decrease the power of $10^{20}$ by $3$ .

$\frac{8540041197781060000000000000}{4.73933649 \cdot 10^{17}}$

Step 8

Divide using scientific notation.

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Step 8.1

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

$(\frac{8540041197781060000000000000}{4.73933649}) (\frac{1}{10^{17}})$

Step 8.2

Divide $8540041197781060000000000000$ by $4.73933649$ .

$1801948692731803660000000003.4 \frac{1}{10^{17}}$

Step 8.3

Move $10^{17}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$1801948692731803660000000003.4 \cdot 10^{- 17}$

Step 9

Move the decimal point in $1801948692731803660000000003.4$ to the left by $27$ places and increase the power of $10^{- 17}$ by $27$ .

$1.80194869 \cdot 10^{10}$

Step 10

The result can be shown in multiple forms.

Scientific Notation:

$1.80194869 \cdot 10^{10}$

Expanded Form:

$18019486927.318$