Precalulus: Expressions with exponents

1. Recall the following properties

x^ax^b = x^a+b

x^a/x^b = x^a-b = 1/x^b-a

(x^a)^b = x^ab

(x y)^a = x^a y^a

(x/y)^a = x^a/y^a

x^-a = 1/x^a

(x/y)^a = (y/x)^{- a}

x⁰ = 1 if x≠0

2. Exercises

Simplify as much as possible each of the following:

x³ x^-2 y + 4 x^-3 y^-2 y^-1/2

x^-2 x^-3/x^-5

(x^1/3 x^-2/3 y³ + x ^{- 1/3}y)/(y² + 1)

[(x² y³² + 1 + x¹⁴)/(y² + 1)]⁰

Solutions