Question

The expression 7^n/7^5 simplifies to 7^p. If n = 18, what is the value of the exponent p? Show your work and explain how you found your answer.

Answer 1

When you divide two powers of the same base, you subtract the exponents:

`(a^b)/(a^c) = a^(b-c)`

This means that, in your case,

`(7^n)/(7^5) = 7^p \iff 7^(n-5) = 7^p \iff n-5 = p`

So, if
`n=18`, the equation becomes

`18-5 = p \iff p = 13`