We are using this property, GM

a^(m/n)  =     ⁿ√[a^m ]

Also remember that    a^m / a ⁿ  =  a ^{(m - n )}

We just need to be careful about the term that the exponent is applied to

a)  4x^1/2 =  4 * x^1/2  =  4 * ²√ [ x¹ ]   =  4 √x

Note that the exponent doesn't apply to the  4   !!!!

b)  (4x)^1/2   .....note that the exponent applies to  (4x)....this is different from the first one...=

√[4x ]  =  2√x

c)   Note  x ^-a  =  1 / x^a

x^-2/5  =   1/ x^2/5  =  1 /  ⁵√[ x² ]

d)  Note that   (8x³)^1/3  = 8^1/3 * (x³)^1/3    =  ³√8  * x¹   =  2x¹

So....we have   

2x^2/3        

____   =        x ^{(2/3 - 1)}  = x^-1/3  =  1 / x^1/3 =    1 / ³√x

  2x¹

e)   a^1/3

     ____               can you finish this one, GM  ?????

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