Expert: Sherry Wallin - 9/8/2010

Question
I have tried to figure out these examples and I can't can you show me please.

Compute and simplify so that only positive remain.
a. 4^-1 y^-2/(4y)^2

b. 4^-1 y^-2/ 4y^2

c.(4y^-2)^-1/(4y)^-2

d.(4y^-2)^-1/ 4y^2


Answer
Jason~

I will work the first one out for you explaining each part:

4^-1 is the same as 1/4^1. Whenever you move a factor up to a numerator or down to a denominator the exponents sign changes (toggles). Since you have -1 in the numerator for the 4 when you move the 4 to the denominator the -1 becomes a +1.

y^-2 is the same as 1/y^2 for the same reason as above.

(4y)^2 = 4^2y^2 = 16y^2

Putting this all together: 4^-1 y^-2/(4y)^2 = 1/(4y^2*16y^2) = 1/64y^4

Math Prof