When an exponent is outside the parentheses, you "distribute" it to the other exponents inside the parentheses.
(4^p)^3 would become 4^3p
(4^1)^3 would become 4^3
When the bases are the same, you just simply add the exponents.
Let's just ignore the bases so it'll look less confusing.
3p + 3 = 15
Subtract 3 from both sides.
3p = 12
Divide both sides by 3.
p = 4
