Answer:
Eric is incorrect. p = 4, not 11.
Explanation:
The left expression simplifies to 4^(3p)*4^3. On the right side we have 4^15. The exponent on the left side must equal the exponent on the right side:
3p + 3 = 15 (the bases are all the same: 4)
Then 3p = 12, and p = 4. Eric is wrong: p is not 11.
We could assume that p = 11 and determine whether or not the equation is true:
(4^11*4^1)^3 = 4^15. Since the bases are all the same (4), focus just on the exponents. Is (11+1)*3 = 15? NO.
Now try p = 4:
(4^4*4^2)^3 = 4^15. Again, focus on the exponents.
Is (4+1)*3 = 15? Is 5*3 = 15? YES. So p = 4 is correct; p = 11 is incorrect.