Question

How do you write `10^-2*10^-8` using only positive exponents?

Answer 1

See entire process below.

Explanation:

First, we will use this rule of exponents to combine the terms:

`x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) +color(blue)(b))`

`10^color(red)(-2) * 10 ^color(blue)(-8) -> 10^(color(red)(-2) + color(blue)(-8)) -> 10^-10`

Now, we can use this rule of exponents to put this into a term with a positive exponent:

`x^color(red)(a) = 1/x^color(red)(-a)`

`10^color(red)(-10) -> 1/10^color(red)(- -10) -> 1/10^10`