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 \(\dfrac{x^2}{x^2}=1\) .

Check your Solutions here.

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