Question

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

Answer 1

Given problem: $\frac{8*10^{-4}}{2*10^2}$.

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

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

$\frac{10^{-4}}{10^2}=10^{-4-(-2)}$

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 $4 \times 10^{-2}$.