How do you simplify #root3(4x^2)color(white)(..)root3(8x^7)#?

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Answer 1 · 2018-04-12T09:33:22

#2^(5/3)x^3#

#sqrtx# = #x^(1/2)#

So we can change the question to

#(4x^2)^(1/3)##xx##(8x^7)^(1/3)#

#4^(1/3)x^(2/3)##xx##8^(1/3)x^(7/3)#

#4=2^2# so #4^(1/3)#=#(2^2)^(1/3)#=#2^(2/3)#

#8^(1/3)=2#

So the question becomes

#2^(2/3)x^(2/3)##xx##2x^(7/3)# = #2^(5/3)x^(9/3)# = #2^(5/3)x^3#

Answer 2 · 2018-04-12T09:39:41

#2^(5/3)x^3#

Expression #= root3(4x^2)root3(8x^7)#

Remember: #root3(a) xx root3(b) = root3(ab)#

Hence, Expression #=root3(4x^2xx8x^7)#

#= root3(32x^9)#

#= root3(32) xx root3(x^9)#

#= root3(2^5) xx root3(x^9)#

#= 2^(5/3)xx (x^9)^(1/3)#

#= 2^(5/3)x^3#