Question

4 xy2 divided by 2give your answers in simplified radical form or standard complex form a plus bi

Answer 1

The expression we have is

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

To simplify the expression, the first step is to separate the fourth root:

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

On the right-hand side, in the numerator, we can no simplify further, but in the denominator, we can use the following law of exponents:

$\sqrt[m]{a^n}=a^{\frac{n}{m}}$

Thus:

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

Since 2/4 is equal to 1/2:

$\sqrt[4]{\frac{x}{y^2}}=\frac{\sqrt[4]{x}}{y^{\frac{1}{2}}}$

Next, we use the same law of exponents:

$a^{\frac{n}{m}}=\sqrt[m]{a^n}$

With n/m as 1/2:

$a^{\frac{1}{2}}=\sqrt[]{a}^{}$

Finally, we simplify the expression to:

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

Answer:

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