SOLUTION: I have tried every way i can think of to simplify this type of equation and have looked through my book, please help me find out how to do these problems. I would really appreciate

Question 20301: I have tried every way i can think of to simplify this type of equation and have looked through my book, please help me find out how to do these problems. I would really appreciate it if someone could help me with this problem.
One of the questions is:
In this and the following problem, simplify the expression and enter the resulting exponent as a fraction, after canceling common factors in numerator and denominator.
(x^2/3 x^1/4)/x^1/7=x^r

where r=?/?
Answer by suresh(20) (Show Source): You can put this solution on YOUR website!
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

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