Neither of them are correct.
This is what Annabelle is doing:
[tex] (4^2+7^5)(4^3+7^2) [/tex]
This is what Navelle is doing:
[tex] (4^27^2)(4^37^2) \implies 4^{2*3}7^{2*5} [/tex]
Navelle is multiplying the exponents. You only do that when you raise an exponent to a power under parenthesis. Annabelle mistook multiplication for addition, and she got her answer as a result. This is the correct way to do it:
[tex] 4^27^5*4^37^2=4^{2+3}*7^{2+5}=4^5*7^7 [/tex]