Question

Which expression is equivalent to `5^-8*5^3`?

Answer 1

`5^-5` or `1/5^5` or `1/3125`

Explanation:

Using the rules for exponents (`color(red)(x^a*x^b = x^(a+b))`):

`5^-8*5^3 -> 5^(-8+3) -> 5^-5`

We can convert further using another rule for exponents (`color(red)(x^-a = 1/x^-a)`):

`5^-5 -> 1/5^5`

And then converting the exponent to a number gives:

`1/(5*5*5*5*5) -> 1/3125`