How do you simplify m^3sqrtmm3m and write it in exponential form?

1 Answer
Jan 7, 2016

m^(7/2)m72

Explanation:

We can move m^3m3 under sqrt()

m^3sqrt(m)=sqrt((m^3)^2*m)=sqrt(m^6*m)=sqrt(m^7)=m^(7/2)m3m=(m3)2m=m6m=m7=m72

remembering that:

a^p*a^q=a^(p+q)apaq=ap+q

(a^p)^q=a^(p*q)(ap)q=apq

root(b)(a^n)=a^(n/b)ban=anb

alternatively:

m^3sqrt(m)=m^3m^(1/2)=m^(3+1/2)=m^((3*2+1)/2)=m^((6+1)/2)=m^(7/2)m3m=m3m12=m3+12=m32+12=m6+12=m72