How do you simplify expressions involving variables such as #(27p^3q^12)^(1/3)#?

1 Answer
Alan P.
Apr 7, 2015

#a^(1/3)# is the third root of #x# or #root(3)(x)#
so what we want to try to do is express the components of #x# as powers of #3# (as much as possible).

Note also that

#root(n)(s*t) = root(n)(s) * root(n)(t)#

For the given example
#(27p^3q^(12))^(1/3)#

#= (3^3* p^3* (q^4)^3)^(1/3)#

#= root(3)(3^3) * root(3)(p^3) *root(3)((q^4)^3)#

#=3pq^4#

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