Question

Calculate 8 ∙ 10-4 divided by 2 ∙ 102. (box after the "10" in answer is for the exponent.). ∙ 10

Answer 1

Given problem:
`(8*10^(-4))/(2*10^2)`.

Solution: We can see that first we have 8 and 2 numbers in front of 10's powers.

So, we need to simplify 8 over 2 first.

If we divide 8 by 2, we get 4.

Now, let us work on 10's and their powers.

`10^(-4)` is being divided by
`10^(2).`

We can apply quotient rule of exponents remaining part.

According to quotient rule of exponents,
`(a^m)/(a^n)=a^(m-n)`

If we apply same rule, we need to subtract exponents of 10's.

`(10^(-4))/(10^2)=10^(-4-(-2))`

If we simplify exponent part -4-(-2), it will give us -4+2 =-2.

So,
`10^(-4-(-2))=10^(-2)`

And final answer would be
`4 * 10^(-2)`.