How do you simplify this expression?

Question

#((2a)^(1/2)(3b)^-2(4a)^(3/5))/((4a)^(-3/2)(3b)^2(2a)^(1/5))#

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Answer 1 · 2018-01-27T18:14:00

#(2^(9/2)a^(12/5))/(81b^4)#

well, I think we can simplify this a bit.
#((2a)^(1/2)(3b)^-2(4a)^(3/5))/((4a)^(-3/2)(3b)^2(2a)^(1/5))#

lets take all the common bases together,

#((2a)^(1/2-1/5)(4a)^(3/5+3/2))/((3b)^(2+2))#

#((2a)^(3/10)(4a)^(21/10))/((3b)^(4))#

#((2a)^(3/10)(2*2a)^(21/10))/((3b)^(4))#

#((2a)^(3/10)2^(21/10)(2a)^(21/10))/((3b)^(4))#

#(2^(21/10)(2a)^(12/5))/((3b)^(4))#

that's the simplest I could get it to, I hope there are no errors, cuz it took a lot of typing. :)

-Sahar

I see that we can go one step further and remove the brackets.

#(2^(21/10)(2a)^(12/5))/((3b)^(4)) = (2^(21/10)(2*a)^(12/5))/((3*b)^(4)) = (2^(21/10)2^(12/5)a^(12/5))/(3^4b^4)#

#(2^(9/2)a^(12/5))/(81b^4)#

EZ as pi