\(b<a<1\)

Quantity A	Quantity B
\(a^3b^6\)	\(b^6\)

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.



Let's test some possible values of a and b


Great explanation. But what if you take an algebraic approach to this and divide both quantities by b^6
We will be left with a^3 and 1. And since a<1
a^3 will be less than 1
I'd be really grateful if you could clear my confusion out

case i: One possible pair of values is \(a=0.5\) and \(b=0\)
We get:
Quantity A: \(a^3b^6=(0.5^3)(0^6) = 0\)
Quantity B: \(b^6=0^6=0\)
In this case, the two quantities are equal

case ii: Another possible pair of values is \(a=0\) and \(b=-1\)
We get:
Quantity A: \(a^3b^6=(0^3)(-1)^6 = 0\)
Quantity B: \(b^6=(-1)^6=1\)
In this case, Quantity B is greater

Answer: D

My Apologies Sir, I am new to this forum and thus had a hard time figuring it out. My doubt is this

Great explanation. But what if you take an algebraic approach to this and divide both quantities by b^6
We will be left with a^3 and 1. And since a<1
a^3 will be less than 1
I'd be really grateful if you could clear my confusion out