How do you simplify #m^3sqrtm# and write it in exponential form?

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Answer 1 · 2016-01-07T22:41:41

#m^(7/2)#

We can move #m^3# under #sqrt()#

#m^3sqrt(m)=sqrt((m^3)^2*m)=sqrt(m^6*m)=sqrt(m^7)=m^(7/2)#

remembering that:

#a^p*a^q=a^(p+q)#

#(a^p)^q=a^(p*q)#

#root(b)(a^n)=a^(n/b)#

alternatively:

#m^3sqrt(m)=m^3m^(1/2)=m^(3+1/2)=m^((3*2+1)/2)=m^((6+1)/2)=m^(7/2)#