SOLUTION: change to rational exponent form. Do not simplify.
∛17^2
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Question 930617: change to rational exponent form. Do not simplify.
∛17^2
Found 2 solutions by ewatrrr, Theo:
Answer by ewatrrr(24785) (Show Source): You can put this solution on YOUR website!
∛17^2 = 17^(2/3)
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.
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