How to solve this? http://i.imgur.com/sE6NF2E.jpg?

The answer is as follows :
https://c1.staticflickr.com/1/593/32341443232_e26de5d4f3_o.png

Hello,

[(8x⁹ y³) /(27x² y¹²)]^(2/3) =

let's first simplify in brackets:

[(8x⁷) /(27y⁹)]^(2/3) =

let's rewrite 8 as 2³ and 27 as 3³:

[(2³x⁷) /(3³y⁹)]^(2/3) =

let's apply the power property (a/b)ⁿ = aⁿ /bⁿ:

(2³x⁷)^(2/3) /(3³y⁹)^(2/3) =

let's apply, in numerator and denominator, the power property (a b)ⁿ = aⁿ bⁿ:

[(2³)^(2/3) (x⁷)^(2/3)] /[(3³)^(2/3) (y⁹)^(2/3)] =

let's apply the power property (aⁿ)ᵐ = aⁿᵐ and let's simplify:

{2^[3(2/3)] x^[7(2/3)]} /{3^[3(2/3)] y^[9(2/3)]} =

[2² x^(14/3)] /{3² y^[3(2)]} =

[4x^(14/3)] /(9y⁶) =

let's split 14/3 as (2 + 12)/3 = 2/3 + 12/3 = (2/3) + 4:

{4x^[(2/3) + 4]} /(9y⁶) =

{4x^[(2/3) + 4]} /(9y⁶) =

finally let's apply the power property aⁿ ⁺ ᵐ = aⁿ aᵐ:

[4x^(2/3) x⁴] /(9y⁶) =

ending with:


[4x⁴ x^(2/3)] /(9y⁶)



I hope it's helpful

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