Final answer:
Alana is not correct in stating that (ab)^3 * (ab)^4 is the same as [(ab)^3]^4.
Step-by-step explanation:
Alana is not correct in stating that (ab)^3 * (ab)^4 is the same as [(ab)^3]^4. To justify this, let's expand both expressions and simplify them:
(ab)^3 * (ab)^4 = (a^3b^3)(a^4b^4) = a^(3+4)b^(3+4) = a^7b^7
[(ab)^3]^4 = (a^3b^3)^4 = (a^(3*4))(b^(3*4)) = a^12b^12
So, we can see that (ab)^3 * (ab)^4 is a^7b^7, whereas [(ab)^3]^4 is a^12b^12. Therefore, Alana's statement is incorrect.