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: (3^(-3)\ xx\ 6^2xx\ sqrt(98))/(5^2\ xx\ root(3)(1/(25))\ xx\ (15)^(-4/3)\ xx\ 3^(1/3))=28sqrt(2)

Simplify : ( 16 xx 10 ^(4) xx 3^(3))/( 6^(5) xx 5^(6))

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

Prove that: (sqrt(3\ xx\ 5^(-3))\ -:root(3)(3^(-1))\ sqrt(5))\ xx\ (3\ xx\ 5^6)^(1/6)\ =3/5

(1/4)^(-10)xx(2/5)^(-10)

Evaluate each of the following: (i)\ (2/(11))^4\ xx\ \ ((11)/3)^2\ xx\ \ (3/2)^3 (ii)\ (1/2)^5\ xx\ ((-2)/3)^4xx\ (3/5)^(-1)

Evaluate: g. 5 (1)/(3) xx 8 (1)/(4) xx 2 (3)/(5)

Simplify. (i) (25 xx t^(-4))/(5^3 xx 10 xx t^(-8)) (t != 0) (ii) (3^(-5) xx 10^(-5) xx 125)/(5^(-7) xx 6^(-5))

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

For the reaction A + B to products, what will be the order of reaction with respect to A and B? {:("Exp",[A](mol L^(-1)),[B](mol L^(-1)),"Initial rate (mol L^(-1) s^(-1))),(1,2.5 xx 10^(-4), 3 xx 10^(-5), 5 xx 10^(-4)),(2,5 xx 10^(-4),6 xx 10^(-5), 4 xx 10^(-3)),(3, 1xx 10^(-3), 6 xx 10^(-5), 1.6 xx 10^(-2)):}