We are given the following expression:
![((2x^3)/(x^4y^2))^2](https://img.qammunity.org/2023/formulas/mathematics/college/tc0zk2jfj3s1fs0m1rp7i10jzkec0usymf.png)
To simplify, we will first use the following property of exponents:
![((a)/(b))^2=((a^2)/(b^2))](https://img.qammunity.org/2023/formulas/mathematics/college/ul5pjsv0iqxntyxmmh1hmfv9dmkn0v0eds.png)
Applying the property we get:
![((2x^3)^2)/((x^4y^2)^2)](https://img.qammunity.org/2023/formulas/mathematics/college/6800t7x9740759jc8w6zixdvsqqswmx4yj.png)
Now we will use the following property:
![(ab)^2=a^2b^2](https://img.qammunity.org/2023/formulas/mathematics/college/d0rdiv5mn63w79nlxvcx82tmhjvs0cqvz4.png)
applying the property:
![(4x^6)/(x^8y^4)](https://img.qammunity.org/2023/formulas/mathematics/college/tbwm7bs6h7vqu2inmbvp7iictvthqfl3vb.png)
Now we cancel out like terms:
![(4)/(x^2y^4)](https://img.qammunity.org/2023/formulas/mathematics/college/u8cxhvf2loapvue4e9r2txm8ooaj2hkga3.png)
Since we can not simplify any further this is the answer.