`(1/2)^6xx(1/2)^3÷(1/2)^8`

Prove that 6^(1//2)xx6^(1//4)xx6^(1//8)...oo=6.

Prove that 6^(1//2)xx6^(1//4)xx6^(1//8)oo=6.

Prove that 6^(1//2)xx6^(1//4)xx6^(1//8)oo=6.

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

simplify (i) (1^(3)+2^(3)+3^(3))^(1/2) (ii) (3/5)^(4)(8/5)^(-12)(32/5)^(6) ,(iii) (1/27)^(-2/3) (vi) [((625)^(-1/2)))^(-1/4)]^(2) ,(v) (9^(1/3)xx27^(-1/2))/(3^(1/6)xx3^(-2/3)) (vi) 64^(-1/3)[64^(1/3)-64^(2/3)] (8^(1/3)xx16^(1/3))/(32^(-1/3)

The value of 2xx2^(1//2)xx2^(1//4)xx2^(1//8)xx ….xx oo is (i) 4 (ii) sqrt(2) (iii) 2sqrt(2) (iv) 8

Find the sum 3/(1xx2)xx1/2+4/(2xx3)xx(1/2)^2+5/(3xx4)xx(1/2)^2+ ton terms.

Simplify : (1/2xx1/4)+\ (1/2xx\ 6)

Simplify (i) {(1/3)^(-2) - (1/2)^(-3)} -: (1/4)^(-2). (ii) (5/8)^(-7) xx (8/5)^(-5).

Prove that: ((0. 6)^0-\ (0. 1)^(-1))/((3/8)^(-1)\ (3/2)^3+\ (-1/3)^(-1))=\ -3/2