How do you simplify #\root [ 3] { 125t ^ { 6} w ^ { 2} }#?

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Answer 1 · 2016-12-13T22:18:14

#5t^2w^(2/3)#

We can rewrite this problem as:

#(125t^6w^2)^(1/3)#

Next we can distribute the exponent on the parenthesis across each term within the parenthesis:

#125^(1/3) (t^6)^(1/3) (w^2)^(1/3)#

We can now use the rule for exponents to solve:

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

#5t^(6*1/3)w^(2*1/3)#

#5t^(6/3)w^(2/3)#

#5t^2w^(2/3)#