SOLUTION: change to rational exponent form. Do not simplify. &#8731;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.

SOLUTION: change to rational exponent form. Do not simplify. &#8731;17^2

SOLUTION: change to rational exponent form. Do not simplify. ∛17^2