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]{(x)/(y^2)}`

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

`\sqrt[4]{(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^{(n)/(m)}`

Thus:

`\sqrt[4]{(x)/(y^2)}=\frac{\sqrt[4]{x}}{y^{(2)/(4)}}`

Since 2/4 is equal to 1/2:

`\sqrt[4]{(x)/(y^2)}=\frac{\sqrt[4]{x}}{y^{(1)/(2)}}`

Next, we use the same law of exponents:

`a^{(n)/(m)}=\sqrt[m]{a^n}`

With n/m as 1/2:

`a^{(1)/(2)}=\sqrt[]{a}^{}`

Finally, we simplify the expression to:

`\sqrt[4]{(x)/(y^2)}=\frac{\sqrt[4]{x}}{\sqrt[]{y}^{}}`

Answer:

`\sqrt[4]{(x)/(y^2)}=\frac{\sqrt[4]{x}}{\sqrt[]{y}^{}}`