Steps:
So here's the rule about raising a power to a power:
- [tex](x^m)^n=x^{m*n}[/tex]
In this case:
[tex](9^p)^5=(9)^{p*5}=9^{5p}[/tex]
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:
[tex]9=3*3=3^2\\\\(3^2)^{5p}[/tex]
Next, apply the rule I mentioned earlier once more:
[tex](3^2)^{5p}=3^{2*5p}=3^{10p}[/tex]
Answer:
In short, your final answer is [tex]3^{10p}[/tex]
