Question

Simplify the expressions below by using the rules of exponents. A.2^4 B.3^0 C.4^6∙4^(-3) D.(2^3 )^2 Answer:

Answer 1

The three rules that we have are:

`x^a*x^b = x^(a + b)`

`(x^a)/(x^b) = x^(a - b)`

`(x^a)^b = x^(a*b)`

Then let's solve the problems:

A) 2^4 = 2^(2*2) = (2^2)^2 = 4^2 = 16.

B) 3^0 = 3^(a - a) = 3^a/3^a = 1. (for any real number a)

From this we can conclude that the power 0 of any number is equal to 1.

C) 4^6*4^(-3) = 4^(6 - 3) = 4^3 = 64

D) (2^3)^2 = 2^(3*2) = 2^6 = 64