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:

$\dfrac{a^b}{a^c} = a^{b-c}$

This means that, in your case,

$\dfrac{7^n}{7^5} = 7^p \iff 7^{n-5} = 7^p \iff n-5 = p$

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

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