How do you use rational exponents to write #x^(1/2)y^(1/6)2^(1/3)# as a single radical expression?

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Answer 1 · 2015-06-14T18:49:36

#x^(1/2)*y^(1/6)*2^(1/3) = root(6)(4x^3y)#

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

#=x^(3/6) *y^(1/6)*2^(2/6)#

#=(x^3)^(1/6) * y^(1/6) * (2^2)^(1/6)#

#=(x^3 * y * 2^2)^(1/6)#

#=(4x^3y)^(1/6)#

#=root(6)(4x^3y)#

...using #x^(ab) = (x^a)^b# and #x^a*y^a = (xy)^a#

How do you use rational exponents to write #x^(1/2)*y^(1/6)*2^(1/3)# as a single radical expression?