# Math Help - Indices, adding for same base

1. ## Indices, adding for same base

I know you add the indices if you're multiplying something with the same base, but what do you do if it's got the same base with a negative sign? (And could you provide extra examples? pretty please?)

Worksheet question:
10^4 * (-0.1)^3

I wrote:

= 10^4 * (-10)^-3

= -(10)^(4-3) <--Is this right?

= -10

2. ## Re: Indices, adding for same base

Correct!
Because $(a\cdot b)^x=a^x \cdot b^x$ you can wright:
$(-10)^{-3}=(-1)^{-3}\cdot(10)^{-3}= -(10)^{-3}$ ...
and so you get:
$-(10^4\cdot 10^{-3})=-10$

3. ## Re: Indices, adding for same base

Yes, just how you add, and subtract variables, you can do the same to exponents with the same base. You could also do it another way. Where $10^4 = 10000 * 10^-^3 = 1/10^3$ which is $1*10000 / 1000 = 10$