Question

Which expression is equivalent to

Answer 1

Answer:

$\frac{\sqrt[4]{3x^2} }{2y}$

Step-by-step explanation:

We can simplify the expression under the root first.

Remember to use  $\frac{a^x}{a^y}=a^{x-y}$

Thus, we have:

$\sqrt[4]{\frac{24x^{6}y}{128x^{4}y^{5}}} \\=\sqrt[4]{\frac{3x^{2}}{16y^{4}}}$

We know 4th root can be written as "to the power 1/4th". Then we can use the property  $(ab)^{x}=a^x b^x$

So we have:

$\sqrt[4]{\frac{3x^{2}}{16y^{4}}} \\=(\frac{3x^{2}}{16y^{4}})^{\frac{1}{4}}\\=\frac{3^{\frac{1}{4}}x^{\frac{1}{2}}}{2y}\\=\frac{\sqrt[4]{3x^2} }{2y}$

Option D is right.