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# Can somone help me solve this? I'm confused...

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Can someone help me solve this? I'm confused... Mar 9, 2019

#1
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Yes she is correct because when you convert it into exponential value like so: \((a^{1/3})^{1/2}\) and then use the Product Property of Exponents you get \(a^{1/6}\) which is equivelent to the 6th root. Also lets say a is 64 and you take the cube root and get 4 and then take the square root of 4 and get 2. Also the 6th oot of 64 is 2. So this shows that they are both equal.

Mar 9, 2019
#2
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As long as " a "  ≥ 0....then

The cube root can be written as a^(1/3)

We are using the property  that    ( a^m)^n  =  a^(m * n)

So....the square root of a cube root is

(a^1/3)^(1/2)  =

(a)^(1/2 * 1/3)  =

a ^(1/6)     ....  i.e.,  the sixth root

This only holds as long as "a" ≥ 0

If "a" <  0.....the  cube root of this is negative...then......  we are taking the square root of a negative.....which is not a real number

Does this make sense, GM ???   Mar 9, 2019
#3
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Ohh! This makes a lot of sense now, Thanks!

-- 7H3_5H4D0W

GAMEMASTERX40  Mar 9, 2019