### Home > AC > Chapter 10 > Lesson 10.4.1 > Problem10-124

10-124.

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?

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.

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

What does $12^{10}$ mean?