Ellie wants to rewrite the expression (a2)2 ∙ (a3)2 as a single exponent of the form an. She claims that n = 36 because 22 · 32 = 4 · 9 = 36. Decide if Ellie is correct. If she is correct, enter 36 below. If she is not correct, enter the correct value of n.

No, Ellie is not correct.
Please assume that I am writing in terms of exponents:
The expression (a2)2. (a3)2 = (a)4.(a)6   [since 2. 2 = 4 and 3. 2 = 6]
                             = (a)(4+6)  [since product of a term with different   
                                                 exponents is equal to the term raised to the 
                                                  power of the sum of the exponents]
                             =(a)10
Therefore the answer is n=10