How do you simplify #(81a^8 b^4)^(1/4)#?

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Answer 1 · 2015-06-20T19:52:54

#(81a^8b^4)^(1/4) = 3a^2abs(b)#

#(81a^8b^4)^(1/4)#

#=(3^4(a^2)^4b^4)^(1/4)#

#=(3^4(a^2)^4abs(b)^4)^(1/4)#

#=((3a^2abs(b))^4)^(1/4)#

Now #3a^2abs(b) >= 0#, so

#=(3a^2abs(b))^(4 * 1/4)#

#=(3a^2abs(b))^1#

#=3a^2abs(b)#