https://cdn.kastatic.org/KA-share/sat/K-5MSA04_FV.pdf
explain page 42 (math noncalc) qn 11 and 12 and please
thanks
9=3^2 so
9^(3/4)=(3^2)(3/4) by substitution
=(3)^(6/4) by exponent rule (x^a)^b=x^ab
=(3)^(3/2) reduce 6/4 to 3/2
=3^(2/2) x 3^(1/2) by exponent rule x^(a+b)=(x^a)(x^b)
=3(3^1/2)=3 sqrt3 Answer D
Background Knowledge:
The volume of a cylinder is directly proportional to the square of the radius. This means if you double the radius, you multiply the volume by r^2= 2^2=4, if you triple the radius, you multiply the volume by 3^2=9, if you multiply the radius by 1/4, you multiply the volume by (1/4)^2=1/16, etc.
The volume of a cylinder is directly proportional to the height. So if you multiply the height by 1/2, you multiply the volume also by 1/2, if you multiply the height by 5, you multiply the volume by 5, etc.
Problem
11) We multiply the radius by 2 and the height by 1/2, so we multiply the volume by 2^2(1/2)=2
The original volume is 22 so the new volume is 2(22)=44. Answer C