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)`