Evaluate Using Scientific Notation ((3.710^2)(4.610^-3))/((1.410^-6)(5.710^8))

$\frac{(3.7 \cdot 10^{2}) \cdot (4.6 \cdot 10^{- 3})}{(1.4 \cdot 10^{- 6}) \cdot (5.7 \cdot 10^{8})}$

Step 1

Multiply $3.7$ by $4.6$ .

$\frac{17.02 (10^{2} \cdot 10^{- 3})}{(1.4 \cdot 10^{- 6}) \cdot (5.7 \cdot 10^{8})}$

Step 2

Multiply $10^{2}$ by $10^{- 3}$ by adding the exponents.

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

$\frac{17.02 \cdot 10^{2 - 3}}{(1.4 \cdot 10^{- 6}) \cdot (5.7 \cdot 10^{8})}$

Subtract $3$ from $2$ .

$\frac{17.02 \cdot 10^{- 1}}{(1.4 \cdot 10^{- 6}) \cdot (5.7 \cdot 10^{8})}$

Step 3

Multiply $1.4$ by $5.7$ .

$\frac{17.02 \cdot 10^{- 1}}{7.98 (10^{- 6} \cdot 10^{8})}$

Step 4

Multiply $10^{- 6}$ by $10^{8}$ by adding the exponents.

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

$\frac{17.02 \cdot 10^{- 1}}{7.98 \cdot 10^{- 6 + 8}}$

Add $- 6$ and $8$ .

$\frac{17.02 \cdot 10^{- 1}}{7.98 \cdot 10^{2}}$

Step 5

Divide using scientific notation.

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

$(\frac{17.02}{7.98}) (\frac{10^{- 1}}{10^{2}})$

Divide $17.02$ by $7.98$ .

$2.13283208 \frac{10^{- 1}}{10^{2}}$

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

$2.13283208 \cdot 10^{- 1 + 2 \cdot - 1}$

Multiply $2$ by $- 1$ .

$2.13283208 \cdot 10^{- 1 - 2}$

Subtract $2$ from $- 1$ .

$2.13283208 \cdot 10^{- 3}$

Evaluate Using Scientific Notation ((3.7*10^2)*(4.6*10^-3))/((1.4*10^-6)*(5.7*10^8))