Question 1037010
i translate this to read:


{{{(5*a^2*b)^(3/5)}}}


this is equivalent to{{{((5*a^2*b)^3)^(1/5)}}} which is equivalent to {{{(5^3*(a^2)^3*b^3)^(1/5)}}} which is equivalent to {{{(125*a^6*b^3)^(1/5)}}} which is equivalent to the fifth root of {{{(125*a^6*b^3)}}}.


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:


{{{(a^b)^c}}} = {{{a^(b*c)}}}


{{{x^(a/b)}}} = {{{(x^a)^(1/b)}}} = the b root of {{{(x^a)}}}.


for example:


{{{(2^2)^3}}} = {{{2^(2*3)}}} = {{{2^6}}} = 64.


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


also:


{{{2^(4/2)}}} = {{{(2^4)^(1/2)}}} = square root of {{{(2^4)}}} = 4.


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