Expert: Socrates - 4/6/2010

Question
1. simplify:
The square root of 3 to the square root of 2 power times the square root of 3 to the negative square root of 2 power.

a)3^-1
b)1/3
c)1
4)3


2. simplify:
The square root of 2 to the square root of 2 power all to the square root of 2 power.

a)4
b)2
c)4 to the square root of 2 power
d)-2


3. simplify:
(The square root of 2 minus 1 to the 2 plus y power) all divided by (the square root of 2 minus 1 to the y power).

a)2^1/2
b)3 - 2(2^1/2)
c)1
d)3+2(2^1/2)


4.simplify:
The square root of 2 to the negative 9 plus 3 power

a) 2 square root of 3 divided by 2
b)8
c)1/2
d)1/8

Answer
1)
c)

add exponents when you multiply and the bases are the same

(3^1/2)^(2^1/2) (3^1/2)^-(2^1/2)  = (3^1/2)^0  = 1  


2)
a)

When a number is raised to an exponent and the entire expression is raised to another exponent ,you multiply exponents

(2^(2^1/2))^(2^1/2) = 2^[(2^1/2)(2^1/2)] = 2^2 = 4


3)
b)

subtract exponents when you divide and the bases are the same


(2^1/2 - 1)^(2+y)  /  (2^1/2 - 1)^y  =  (2^1/2 - 1)^2 = 2-(2)(2^1/2)+ 1 = 3-(2)(2^1/2)


4)

d)


a number to a negative exponent is one over the number to the positive exponent

(2^1/2)^(-9+3) = (2^1/2)^(-6) = 2^-3 = 1/2^3  = 1/8