Lacey and Haley are simplifying expressions.  

1. Haley simplified $x^3\cdot x^2$ and gets $x^5$^. Lacey simplified $x^3+x^2$ and got the same result! However, their teacher told them that only one simplification is correct. Who simplified correctly and how do you know?

   Answer (a):

   Haley is correct because you cannot add unlike terms.

2. Haley simplifies $3^5\cdot4^5$ and gets the result $12^{10}$, but Lacey is not sure. Is Haley correct? Be sure to justify your answer.

   Hint (b):

   $3^5\cdot4^5=3\cdot3\cdot3\cdot3\cdot3\cdot4\cdot4\cdot4\cdot4\cdot4$

   What does $12^{10}$ mean?