EXPS 1 | Lesson 2 | Explore (Division)

Expand each expression and simplify completely.

1. $$\dfrac{x^5}{x^2}$$
2. $$\dfrac{x^3y}{x^5}$$
3. $$\dfrac{5x^3}{25xy^2}$$

1. Use words to generalize a third rule of exponents for when expressions with the same base are divided.
2. Show a proof for the statement you generalized in Question 4. (Use the proofs from “Try This!” as an example.)

1. Use the exponent rule that you generalized to verify that $$\dfrac{3x^5}{6x^3}=\dfrac{x^2}{2}$$.
2. Use the exponent rule that you generated to simplify$$\dfrac{x^{-2}}{x^3}$$.
3. Use the exponent rule that you generalized to show mathematically why $$\dfrac{x^2}{x^2}=1$$ .