Question

Apply the laws of exponents, calculate the result and express the result in scientific notation, and as a decimal:
((4.1·103)(2.8·10−7))/(3.1·10−5)

The result in scientific notation is_ *10^_. The result as a decimal is_.

Answer 1

We are given

$\frac{(4.1\times 10^{3})(2.8\times 10^{-7})}{(3.1\times 10^{-5})}$

We can move like terms altogether

$\frac{(4.1\times 10^{3})(2.8\times 10^{-7})}{(3.1\times 10^{-5})}=\frac{4.1\times 2.8}{3.1}\times \frac{10^{3}\times 10^{-7}}{10^{-5}}$

now, we can use property of exponent

$a^m\times a^n=a^{m+n}$

$=\frac{4.1\times 2.8}{3.1}\times \frac{10^{3-7}}{10^{-5}}$

We can use another exponent property

$\frac{a^m}{a^n} =a^{m-n}$

so, we get

$=\frac{4.1\times 2.8}{3.1}\times 10^{3-7+5}$

$=\frac{4.1\times 2.8}{3.1}\times 10^{1}$

$=3.70323\times 10^{1}$

So, the result in scientific notation is

$=3.70323\times 10^{1}$..........Answer

So, the result as a decimal is

$=37.0323$.............Answer