Question

express (9^p)^5 with a prime number base in exponential form

Answer 1

Steps:

So here's the rule about raising a power to a power:

• $(x^m)^n=x^{m*n}$

In this case:

$(9^p)^5=(9)^{p*5}=9^{5p}$

However, we aren't finished since 9 is not a prime number. Now, we are going to use prime factorization to break down this number as such:

$9=3*3=3^2\\\\(3^2)^{5p}$

Next, apply the rule I mentioned earlier once more:

$(3^2)^{5p}=3^{2*5p}=3^{10p}$

Answer:

In short, your final answer is $3^{10p}$