Exponents
Out of context: Reply #10
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- drgss0
I think both questions are solved by factorization
In first question all answers are multiples of 18, in the form
r * t = k * 18, where k = 1,2,6,9 or 18As people have pointed out the first equation is simplified to
r * r * t = 18^3, setting in r * t = k * 18
r * k * 18 = 18^3
r * k = 18^2
k = 18^2 / r
so basically we are looking for integer divisors of 18^2 = 2*2*3*3*3*3 up to k = 18, which are
2, 3, 4, 6, 9, 12, 18 etc
we have 4 matches
k = 2 which gives r = 162 and t = around 0.5, which is not an integer
k = 6 , r = 54 and t = 2
k = 9, r = 36 and t = 4.5, not an integer
k = 18, r = 18, t = 18, which is not an option since r must be r > t
so the answer is r = 54 and t = 2And the second question
a * a * a * b * b = 432 = 2 * 2 * 2 * 2 * 3 * 3 * 3 = 3 * 3 * 3 * (2 * 2) * (2 * 2)
so a = 3 and b = 4