Question

Part 1:
Show the expanded form and simplification of x^6/x^2. Explain in your own words how you can simplify x^6/x^2 without having to write the expanded form.

Part 2:

Create your own fraction with like bases, coefficients, and show its simplification.

Answer 1

#1.
x^6 / x^2
= (x * x * x * x * x * x) / (x * x) when expanded
= (x * x * x * x) after cancelling x terms in the numerator and denominator
= x^4

"You can simplify x^6 / x^2 without having to write the expanded form by subtracting the exponent of the numerator by the exponent of like-based factors in the denominator. In this example, the answer is x^(6 - 2) = x^4."

#2.
(9y^5) / (3y^2)
= (3^2 * y^5) / (3^1 * y^2)
= 3^(2-1) * y^(5-2)
= 3^1 * y^3
= 3y^3