Question

How do you simplify this expression?

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

Answer 1

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

Explanation:

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