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 $m^(7/3)$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$color(blue)("Shortcut method")$

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

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