How do you write #(3sqrtm)^7# as an exponential form?

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Answer 1 · 2016-01-16T21:56:29

Assumption: you mean: #(root(3)(m))^7#

#color(blue)(m^(7/3))#

Given: #(root(3)(m))^7#

#color(blue)("Explained from 'sort of' first principles")#

Consider inside the brackets only:

#root(3)(m)-> m^(1/3)#

Substituting this back inside the original expression

#(m^(1/3))^7#

This is: #m^(1/3)xxm^(1/3)xxm^(1/3)xxm^(1/3)xxm^(1/3)xxm^(1/3)xxm^(1/3)#

#m^((1/3+1/3+1/3+1/3+1/3+1/3+1/3))#

Which is #m^(7/3)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Shortcut method")#

#(root(3)(m))^7= m^(1/3xx7)=m^(7/3)#