`[8^(-2/3)times2^(1/2)times25^(-5/4)]÷[32^(-2/5)times125^(-5/6)] =sqrt2`

5^(2)times25^(3)times625=(5)^(?)

(6^(3)times7^(4)times8^(5))/(4^(3)times9^(2)times16)

3^(-5)times10^(-4)times(5^(4))/(5^(2))times6^(-5)=

25^(32)times16^(-34)times5^(-2)times1024^(32)

Prove that . (i) [8^(-(2)/(3)) xx 2^((1)/(2))xx 25^(-(5)/(4))] div[32^(-(2)/(5)) xx 125 ^(-(5)/(6)) ] = sqrt(2) (ii) ((64)/(125))^(-(2)/(3)) = (1)/(((256)/(625))^((1)/(4)))+ (sqrt(25))/(root3(64)) = (65)/(16) (iii) [7{(81)^((1)/(4)) +(256)^((1)/(4))}^((1)/(4))]^(4) = 16807 .

(1/3times-1/2)times5/6 = (5/6 times 1/3)times-1/2

(8^(-1)times(5)^(3))/(2^(-4))

[((-2)/(-3))times(1)/(5)]times((-2)/(7))=((-2)/(-3))times[(1)/(5)times((-2)/(7))]

((5^(3))^(-2)times(5^(2))^(-3)times(6)^(5))/((2)^(3)times(3)^(2)times(5)^(5))

Simplify -(2)/(3)times5(1)/(2)times2times7(5)/(6)times(9)/(11)