4th root of 256x^2y^16

Answer 1

To find the 4th root of the expression \( 256x^2y^{16} \), we can break it down into its components:

1. Find the 4th root of 256: \[ 256 = 4^4 \quad \text{(since } 4 \times 4 \times 4 \times 4 = 256\text{)} \] Therefore, the 4th root of 256 is: \[ \sqrt[4]{256} = \sqrt[4]{4^4} = 4 \]

2. Find the 4th root of \( x^2 \): \[ \sqrt[4]{x^2} = x^{2/4} = x^{1/2} = \sqrt{x} \]

3. Find the 4th root of \( y^{16} \): \[ \sqrt[4]{y^{16}} = y^{16/4} = y^4 \]

Now combine all these results together: \[ \sqrt[4]{256x^2y^{16}} = 4 \cdot \sqrt{x} \cdot y^4 \]

Thus, the final answer is: \[ 4y^4\sqrt{x} \]

Answer 2

so 4x^1/2y^4

Answer 3

Yes, you are correct!

The expression can be written as: \[ 4y^4x^{1/2} \]

For clarity, if we want to emphasize the exponent in the form of a fraction, it can also be written as: \[ 4y^4x^{\frac{1}{2}} \]

Both forms are equivalent and convey the same mathematical meaning. Thank you for the clarification!