Question

Which expression is equivalent to RootIndex 4 StartRoot StartFraction 24 x Superscript 6 Baseline y Over 128 x Superscript 4 Baseline y Superscript 5 Baseline EndFraction EndRoot? Assume x not-equals 0 and y
StartFraction RootIndex 4 StartRoot 3 EndRoot Over 2 x squared y EndFraction
StartFraction x (RootIndex 4 StartRoot 3 EndRoot) Over 4 y squared EndFraction
StartFraction RootIndex 4 StartRoot 3 EndRoot Over 4 x y squared EndFraction
StartFraction RootIndex 4 StartRoot 3 x squared EndRoot Over 2 y EndFraction

Answer 1

Answer:

The expression is equivalent to$A=\sqrt[4]{\frac{24\ x^{6}\ y}{128\ x^{4}\ y^{5}}}$ is  $\frac{\sqrt[4]{3}}{2}}\times \frac{\sqrt{x}}{y}$.

Step-by-step explanation:

The expression provided is:

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

Simplify the expression A as follows:

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

   $=\sqrt[4]{\frac{24}{128}\times x^{(6-4)}\times y^{(1-5)}}\\\\=\sqrt[4]{\frac{3}{16}\times x^{2}\times y^{-4}}\\\\=[\frac{3}{16}\times x^{2}\times y^{-4}]^{1/4}\\\\=[\frac{3}{16}]^{1/4}\times x^{(2\times (1/4))}\times y^{(-4\times (1/4))}\\\\=\frac{\sqrt[4]{3}}{2}}\times x^{1/2}\times y^{-1}\\\\=\frac{\sqrt[4]{3}}{2}}\times \frac{\sqrt{x}}{y}$

Thus, the expression is equivalent to$A=\sqrt[4]{\frac{24\ x^{6}\ y}{128\ x^{4}\ y^{5}}}$ is  $\frac{\sqrt[4]{3}}{2}}\times \frac{\sqrt{x}}{y}$.

Answer 2

Answer:

The answer is D, I just took it on edgen.  Known as RootIndex 4 StartRoot 3 x squared EndRoot Over 2 y       or         4 root 3x^2/ 2y

Step-by-step explanation: