`(16 a^4)^(1/2) xx ( 8 a^6)^ (2/3)`

Prove that : 2^(1/4)xx4^(1/8)xx8^(1/16)xx16^(1/32)xx ....... → oo =2 .

Simplify: (i)\ ((25)^(3/2)\ xx\ (243)^(3/5))/((16)^(5/4)\ xx\ (8)^(4/3))

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

What is the value of ((3)/(4) div (9)/(32) +(4)/(3) xx (2)/(3) " of "(27)/(16))/((1)/(2) xx ((8)/(2) -2) div (4)/(9) +((1)/(3)+(1)/(6))) ? (a) (10)/(3) (b) (13)/(2) (c) (25)/(2) (d) (31)/(2)

Simplify : ((25)^((3)/(2)) xx ( 343 )^((1)/(5)))/( 16^((5)/(4)) xx 8^((4)/(3)) xx 7^((3)/(5)))

The value of the product 6^(1/2)xx6^(1/4)xx^(1/8)xx6^(1/16) . . . . .oo is

Evaluate ((25)^(3//2)xx(243)^(3//5))/((16)^(5//4)xx(8)^(4//3))

Solve the following equations: (i) 3^(x+1)=27 xx 3^4 (ii)4^(2x)=(16 3)^(-6/y)=(sqrt(8))^2 (iii) 3^(x-1) xx 5^(2y-3)=225 (iv) 8^(x+1)=16^(x+2) and, (v) (1/2)^(3+x)=(1/4)^(3y) 4^(x-1) xx (0. 5)^(3-2x)=(1/8)^x sqrt(a/b)=(b/a)^(1-2x ) , where a , b are distinct positive primes.

Multiply and express as a mixed fraction : (a) 3xx(5)(1)/(5) (b) 5xx(6)(3)/(4) (c) 7xx(2)(1)/(4) (d) 4xx(6)(1)/(3)( e) (3)(1)/(4)xx6( f )(3)(2)/(3)xx8

{(81)^(-3/4)xx((16)^(1/4))/(6^(-2))xx(1/27)^(-4/3)}^(1/3)=