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

`((4.1* 10^(3))(2.8* 10^(-7)))/((3.1* 10^(-5)))`

We can move like terms altogether

`((4.1* 10^(3))(2.8* 10^(-7)))/((3.1* 10^(-5)))=(4.1* 2.8)/(3.1)* (10^(3)* 10^(-7))/(10^(-5))`

now, we can use property of exponent

`a^m* a^n=a^(m+n)`

`=(4.1* 2.8)/(3.1)* (10^(3-7))/(10^(-5))`

We can use another exponent property

`(a^m)/(a^n) =a^(m-n)`

so, we get

`=(4.1* 2.8)/(3.1)* 10^(3-7+5)`

`=(4.1* 2.8)/(3.1)* 10^(1)`

`=3.70323* 10^(1)`

So, the result in scientific notation is

`=3.70323* 10^(1)`..........Answer

So, the result as a decimal is

`=37.0323`.............Answer