Answer:
The error in the work shown takes place in the third step. When they are attempting to write the radicand as a single fraction. Instead of having y^4 in the parentheses being cubed, they have y^3 in the parentheses being raised to the fourth. From there, they cross out the cubed with the cube root, but you cant do that since the y is actually being taken to the fourth.
Step-by-step explanation:
The error lies in the last step where there is cancellation of cube root with 4th power of y, which is not correct.
[tex]^3\sqrt{\dfrac{x^3(y^{12})}{4^3}}[/tex]
[tex]\begin{aligned} ^3\sqrt{\dfrac{x^3(y^{12})}{4^3}} &= {\dfrac{^3\sqrt{x^3(y^{12}})}{^3\sqrt{4^3}}\\&= ^{\dfrac{^3\sqrt{x^3(y^{4})^3}}{^3\sqrt{4^3}}\\&=\dfrac{xy^4}{4}\\\end{aligned}[/tex]
We can't say that the second last expression was wrong since it is completely correct. But we take out cubic power outside so as to cancel out the cube root that we have.
Thus, the correct simplification will lead to [tex]\dfrac{xy^4}{4}[/tex]. And thus, the last step is wrong as it does wrong cancellation of cubic root with 4th power of y.
Learn more about roots and power here:
https://brainly.com/question/2279789
