Can anyone help me with this problem?√5^2/3 = ( √5^1/3)^2 = 5-1/3 My text book doesn't explain the steps necessary to get to the answer.  I am confused by the exponent 2/3 in the problem.

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If I'm not mistaken the last expression in your equation should be 5^1/3 not 5-1/3.The key to these problems is to remember that a fractional exponent can be expressed as a root. For example, 5^(1/2) is the same as the square root of 5, and 5^(1/3) is the cube root of 5. Also, when you are doing multiple exponents, (5^2)^3 = 5^(2*3) = (5^3)^2 = 5^6.So, something like 5^(2/3) is the same as (5^(1/3))^2, and (5^2)^(1/3).Also (5^2)^(1/2) = 5^((1/2)*2) = 5^(2/2) = 5^1 = 5.So in your problem, you have √5^2/3 = (5^2/3)^(1/2) = (5^(1/3)*2)^(1/2) = (((5^(1/3))^2)^(1/2)= (5^(1/3)^(2/2) = (5^1/3)^1 = 5^1/3This will look more clear to you if you write it out the usual way without using the ^ sign.