SOLUTION: Rewrite without rational exponents and simplify if possible (5a^2b)^3/5

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Question 1037010: Rewrite without rational exponents and simplify if possible
(5a^2b)^3/5
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i translate this to read:

%285%2Aa%5E2%2Ab%29%5E%283%2F5%29

this is equivalent to%28%285%2Aa%5E2%2Ab%29%5E3%29%5E%281%2F5%29 which is equivalent to %285%5E3%2A%28a%5E2%29%5E3%2Ab%5E3%29%5E%281%2F5%29 which is equivalent to %28125%2Aa%5E6%2Ab%5E3%29%5E%281%2F5%29 which is equivalent to the fifth root of %28125%2Aa%5E6%2Ab%5E3%29.

i confirmed by assigning the value of 7 to a and the value of 9 to b and evaluated the original expression and the final expression.

i got the original expression = 101.4016814
i got the final expression = 101.4016814

since the values are the same, i assumed that the solution is correct.

the basic concepts used are:

%28a%5Eb%29%5Ec = a%5E%28b%2Ac%29

x%5E%28a%2Fb%29 = %28x%5Ea%29%5E%281%2Fb%29 = the b root of %28x%5Ea%29.

for example:

%282%5E2%29%5E3 = 2%5E%282%2A3%29 = 2%5E6 = 64.

since 2^2 = 4 and 4^3 = 64, this confirms the concept is correct.

also:

2%5E%284%2F2%29 = %282%5E4%29%5E%281%2F2%29 = square root of %282%5E4%29 = 4.

since 2^4 = 16 and the square root of 16 is equal to 4, this confirms the concept is correct.