Evaluate Using Scientific Notation ((1610^6)(910^13))/((310^-6)(410^-11))

$\frac{(16 \cdot 10^{6}) (9 \cdot 10^{13})}{(3 \cdot 10^{- 6}) (4 \cdot 10^{- 11})}$

Step 1

Multiply $16$ by $9$ .

$\frac{144 (10^{6} \cdot 10^{13})}{(3 \cdot 10^{- 6}) (4 \cdot 10^{- 11})}$

Step 2

Multiply $10^{6}$ by $10^{13}$ by adding the exponents.

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

$\frac{144 \cdot 10^{6 + 13}}{(3 \cdot 10^{- 6}) (4 \cdot 10^{- 11})}$

Add $6$ and $13$ .

$\frac{144 \cdot 10^{19}}{(3 \cdot 10^{- 6}) (4 \cdot 10^{- 11})}$

Step 3

Multiply $3$ by $4$ .

$\frac{144 \cdot 10^{19}}{12 (10^{- 6} \cdot 10^{- 11})}$

Step 4

Multiply $10^{- 6}$ by $10^{- 11}$ by adding the exponents.

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

$\frac{144 \cdot 10^{19}}{12 \cdot 10^{- 6 - 11}}$

Subtract $11$ from $- 6$ .

$\frac{144 \cdot 10^{19}}{12 \cdot 10^{- 17}}$

Step 5

Divide using scientific notation.

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

$(\frac{144}{12}) (\frac{10^{19}}{10^{- 17}})$

Divide $144$ by $12$ .

$12 \frac{10^{19}}{10^{- 17}}$

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

$12 \cdot 10^{19 - 17 \cdot - 1}$

Multiply $- 17$ by $- 1$ .

$12 \cdot 10^{19 + 17}$

Add $19$ and $17$ .

$12 \cdot 10^{36}$

Step 6

Move the decimal point in $12$ to the left by $1$ place and increase the power of $10^{36}$ by $1$ .

$1.2 \cdot 10^{37}$

Evaluate Using Scientific Notation ((16*10^6)(9*10^13))/((3*10^-6)(4*10^-11))