Prove that: `3^(1/2)xx3^(1/4)xx3^(1/8)xx...=3`

Prove that : 3^(1/2)xx3^(1/4)xx3^(1/8)xx.......... to oo=3 .

Prove that 3^((1)/(2)) xx 3^((1)/(4)) xx 3^((1)/(8)) …..= 3

Prove that: (2^(1/2)\ xx\ 3^(1/3)\ xx\ 4^(1/4))/(10^(-1/5)\ xx\ 5^(3/5))\ -:(3^(4/3)\ xx\ 5^(-7/5))/(4^(-3/5)\ xx\ 6)=10

Prove that 1/3^2xx1/3^4xx1/3^8............=3

Prove that 1^(1)xx2^(2)xx3^(3)xx xx n^(n)<=[(2n+1)/3]^(n(n+1)/2),n in N

Prove that: (1/4)^(-2)-3\ xx\ 8^(2/3)\xx\ 4^0+\ (9/(16))^(-1/2)=(16)/3

Fill in the blanks. 2xx(3^(1)xx3^(-1)xx3^(-1)xx3^(0))= ______.

Prove that 1/4^3xx1/4^9xx1/4^(27)……………..=8

4^(1/3)xx[2^(1/3)xx3^(1/2)]div 9^(1/4)=

Prove that 1^1xx2^2xx3^3xx...xn^nlt ((2n+1)/(3))^((n(+1))/(2)