(m^1/4n^1/2) ^2(m^2n^3) ^1/2

Question

I am totally confused

 

In this discussion, you will simplify and compare equivalent expressions written both in radical form and with rational (fractional) exponents.
using the following words
 
Principal Root

Product rule

Quotient rule

Reciprocal

nth root 

Answer 1

( m^1/4 ^ n ^1/2) ^2 * ( m^2 n^3) ^1/2 =

 

  ( m ^1/2 * n)  * ( m * n^3/2) =

 

   m^3/2 * n ^ 5/2    or  √(m^3. n^5)

 

    Operation of Exponent    a ^ m . a ^n = a ^ ( m +n)

                                       

                                     ( a^m ) ^n = a ^(mn)  

                                        

                                        Is used.