Expand each expression and simplify completely.
- \(\dfrac{x^5}{x^2}\)
- \(\dfrac{x^3y}{x^5}\)
- \(\dfrac{5x^3}{25xy^2}\)
- Use words to generalize a third rule of exponents for when expressions with the same base are divided.
- Show a proof for the statement you generalized in Question 4. (Use the proofs from “Try This!” as an example.)
- Use the exponent rule that you generalized to verify that \(\dfrac{3x^5}{6x^3}=\dfrac{x^2}{2}\).
- Use the exponent rule that you generated to simplify\(\dfrac{x^{-2}}{x^3}\).
- Use the exponent rule that you generalized to show mathematically why \(\dfrac{x^2}{x^2}=1\) .
