### Home > GB8I > Chapter 1 Unit 1 > Lesson INT1: 1.3.1 > Problem1-69

1-69.

Lacey and Haley are rewriting expressions in an equivalent, simpler form.

1. Haley simplified $x^3 · x^2$and got $x^5$. 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. Haley used the product rule with exponents.
Since each factor has the same base, we simply add the exponents.

2. Haley simplifies $3^5 \cdot 4^5$ and gets the result $12^{10}$, but Lacey is not sure. Is Haley correct? Be sure to justify your answer.

If Haley is correct, then $2^1\cdot3^1 = 6^2$
Which would imply that $2\cdot3 = 36!$
Clearly this counterexample provides a hint of why Haley is wrong.