Question

4th root of 256x^2y^16

Answer 1

so 4x^1/2y^4

Answer 2

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 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!