Question 20301
Given:
(x^2/3 x^1/4)/(x^1/7)=x^r.

Law of indices:
 x^m * x^n = x^(m+n)-------(1)

 x^x / x^n = x^(m-n) ------(2)

Law of exponents:
x^m = x^n if and only if m = n -----(3)

x^r = x^(2/3 + 1/4 )/x^1/7  (Using (1))

    = x^(11/12)/x^1/7       (Simplifying by LCD Method)

    = x^(11/12 - 1/7 )       (Using (2))

    = x^(65/84)

Therefore, x^r = x^65/84

---->  r = 65 / 84  (Using 3)

Hence r = 65 /84