Question 930617
a rational exponent is an exponent with a numerator and a denominator.
 

the numerator of the exponent tells you the power.


the denominator of the exponent tells you the root.


some examples will help you to understand.


5^2 = 5 squared = 5 to the power of 2 = 5*5 = 25.


5^3 = 5 cubed = 5 to the power of 3 = 5*5*5 = 125.


25^(1/2) = square root of (25) = 25 to the root of 2 = 5.


125^(1/3) = the cube root of 125 = 125 to the root of 3 = 5.


the root is the inverse of the power.


if 5^2 = 25, then 25^(1/2) = 5


if 5^3 = 125, then 125^(1/3) = 5


in your problem, this is what you can do.


cube root of (17^2) is equal to (17^2)^(1/3) = 17^(2 * 1/3) = 17^(2/3)


(cube root of 17)^2 is equal to (17^(1/3))^2 = 17^(1/3 * 2) = 17^(2/3)


the rules of exponent arithmetic are that:


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


that's the rule that was applied.