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Can someone help me solve this? I'm confused...

 Mar 9, 2019
 #1
avatar+14 
+2

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
avatar+105327 
+1

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 ???

 

 

cool cool cool

 Mar 9, 2019
 #3
avatar+49 
-6

Ohh! This makes a lot of sense now, Thanks!

 

-- 7H3_5H4D0W

GAMEMASTERX40  Mar 9, 2019

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