Basic Math Examples

$\frac{(7 \cdot 10^{- 7}) (8.5 \cdot 10^{4})}{(5 \cdot 10^{- 2}) (1.7 \cdot 10^{11})}$

Step 1

Multiply $7$ by $8.5$ .

$\frac{59.5 (10^{- 7} \cdot 10^{4})}{(5 \cdot 10^{- 2}) (1.7 \cdot 10^{11})}$

Step 2

Multiply $10^{- 7}$ by $10^{4}$ 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.

$\frac{59.5 \cdot 10^{- 7 + 4}}{(5 \cdot 10^{- 2}) (1.7 \cdot 10^{11})}$

Step 2.2

Add $- 7$ and $4$ .

$\frac{59.5 \cdot 10^{- 3}}{(5 \cdot 10^{- 2}) (1.7 \cdot 10^{11})}$

Step 3

Multiply $5$ by $1.7$ .

$\frac{59.5 \cdot 10^{- 3}}{8.5 (10^{- 2} \cdot 10^{11})}$

Step 4

Multiply $10^{- 2}$ by $10^{11}$ by adding the exponents.

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Step 4.1

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

$\frac{59.5 \cdot 10^{- 3}}{8.5 \cdot 10^{- 2 + 11}}$

Step 4.2

Add $- 2$ and $11$ .

$\frac{59.5 \cdot 10^{- 3}}{8.5 \cdot 10^{9}}$

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.

$(\frac{59.5}{8.5}) (\frac{10^{- 3}}{10^{9}})$

Step 5.2

Divide $59.5$ by $8.5$ .

$7 \frac{10^{- 3}}{10^{9}}$

Step 5.3

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

$7 \cdot 10^{- 3 + 9 \cdot - 1}$

Step 5.4

Multiply $9$ by $- 1$ .

$7 \cdot 10^{- 3 - 9}$

Step 5.5

Subtract $9$ from $- 3$ .

$7 \cdot 10^{- 12}$