Question

Applying Properties of Exponents In Exercise, use the properties of exponents to simplify the expression.

(a) (e5)2
(b) e^3/e^5
(c) (e4) (e3/2)
(d) (e2) - 4

Answer 1

a) e¹⁰

b) 1/e²

c) e^(11/2)

d) 1/e⁸

Explanation:

a) The power of a power is the multiplication of the eponents, thus

(e⁵)² = e^(5*2) = e¹⁰

b) When you divide powers, you can take the power of the substraction, hence

e³/e⁵ = e^(3-5) = e⁻² = 1/e²

c) When you multiply powers, you have to sum the exponents, as a result

e⁴*e^(3/2) = e^(4+3/2) = e^(11/2)

d) We use the same property for item a

(e²)⁻⁴ = e^(2*-4) = e⁻⁸ = 1/e⁸