Evaluate Using Scientific Notation ((910^-20)(4.110^35))/(1.2*10^40)

$\frac{(9 \cdot 10^{- 20}) (4.1 \cdot 10^{35})}{1.2 \cdot 10^{40}}$

Step 1

Multiply $9$ by $4.1$ .

$\frac{36.9 (10^{- 20} \cdot 10^{35})}{1.2 \cdot 10^{40}}$

Step 2

Multiply $10^{- 20}$ by $10^{35}$ by adding the exponents.

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

$\frac{36.9 \cdot 10^{- 20 + 35}}{1.2 \cdot 10^{40}}$

Add $- 20$ and $35$ .

$\frac{36.9 \cdot 10^{15}}{1.2 \cdot 10^{40}}$

Step 3

Divide using scientific notation.

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

$(\frac{36.9}{1.2}) (\frac{10^{15}}{10^{40}})$

Divide $36.9$ by $1.2$ .

$30.75 \frac{10^{15}}{10^{40}}$

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

$30.75 \cdot 10^{15 + 40 \cdot - 1}$

Multiply $40$ by $- 1$ .

$30.75 \cdot 10^{15 - 40}$

Subtract $40$ from $15$ .

$30.75 \cdot 10^{- 25}$

Step 4

Move the decimal point in $30.75$ to the left by $1$ place and increase the power of $10^{- 25}$ by $1$ .

$3.075 \cdot 10^{- 24}$

Evaluate Using Scientific Notation ((9*10^-20)(4.1*10^35))/(1.2*10^40)