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I do not follow this solution:

Simplify the following:

the 4th root of 3 divided by the 4th root of 5

The solution manual says to multiply the top and bottom by the 4th root of 5 cubed. I don't see why. Why not just multiply the top and bottom by the 4th root of 5?

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They want to you rationalize the denominator.

The 4th root of 3 divided by the 4th root of 5 is of course the 4th root of (3/5).

However, one often wants to have a rational denominator. To rationalize the denominator, you need to multiply both numerator and denominator by 4th root of 5 cubed (i.e. 5^(3/4))so that your denominator ends up being 5, a rational number:

(3/5)^(1/4)= (3/5)^(1/4) * (5/5/)^(3/4) = [3^(1/4) * 5^(3/4)] /5

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They want to you rationalize the denominator.

The 4th root of 3 divided by the 4th root of 5 is of course the 4th root of (3/5).

However, one often wants to have a rational denominator. To rationalize the denominator, you need to multiply both numerator and denominator by 4th root of 5 cubed (i.e. 5^(3/4))so that your denominator ends up being 5, a rational number:

(3/5)^(1/4)= (3/5)^(1/4) * (5/5/)^(3/4) = [3^(1/4) * 5^(3/4)] /5

No wonder your 15 year old is in Calculus.

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