Question

How do you write `5^-8*5^-7` using only positive exponents?

Answer 1

First, we will use this rule of exponents to combine the `5` terms:

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

`5^color(red)(-8) xx 5^color(blue)(-7) = 5^(color(red)(-8) +color(blue)(-7)) = 5^-15`

Now, we can use this rule of exponents to eliminate the negative exponent:

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

`5^color(red)(-15) = 1/5^color(red)(- -15) = 1/5^15`