How do you simplify #\sqrt { 27x ^ { 6} w ^ { 3} }#?

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Answer 1 · 2016-12-18T14:23:03

#3^(3/2)x^3w^(3/2)#

Because #color(red)(sqrt(a) = a^(1/2))# we can rewrite this expression as:

#(27x^6w^3)^(1/2)#

Next we can rewrite #27# as #3^3# which gives us:

#(3^3x^6w^3)^(1/2)#

Finally, one of the rules of exponents is:

#color(red)((x^a)^b = x^(a*b))#

Applying this rule across the entire expression gives:

#3^(3*1/2)x^(6*1/2)w^(3*1/2)#

#3^(3/2)x^3w^(3/2)#