Simplify the radical 128x4y9−−−−−−−√ .(1 point) Responses 14x2y46y−−√ 14 x squared y to the 4th power square root of 6 y 8x3y62xy3−−−−√ 8 x cubed y to the 6th power square root of 2 x y cubed end root 14x3y62xy3−−−−√ 14 x cubed y to the 6th power square root of 2 x y cubed end root 8x2y42y−−√

To simplify the radical expression \( \sqrt{128x^4y^9} \), we can break it down as follows:

1. **Factor the radicand**:
- \( 128 = 64 \cdot 2 = 8^2 \cdot 2 = 4^2 \cdot 8 = 2^7 \)
- For \( x^4 \), it is already simplified.
- For \( y^9 \), we can write it as \( (y^4)^2 \cdot y \) (since 9 is an even number).

2. **Rewrite the expression under the square root**:
\[
\sqrt{128x^4y^9} = \sqrt{(8^2 \cdot 2) \cdot x^4 \cdot (y^4)^2 \cdot y}
\]

3. **Separate the perfect squares from the rest**:
\[
= \sqrt{8^2} \cdot \sqrt{x^4} \cdot \sqrt{(y^4)^2} \cdot \sqrt{2} \cdot \sqrt{y}
\]

4. **Simplify the square roots**:
- \( \sqrt{8^2} = 8 \)
- \( \sqrt{x^4} = x^2 \)
- \( \sqrt{(y^4)^2} = y^4 \)

5. **Combine everything together**:
\[
= 8x^2y^4\sqrt{2y}
\]

Now, we can compare to the responses provided. The simplified result \( 8x^2y^4\sqrt{2y} \) matches with the option that represents this expression.

Therefore, the final simplified form of \( \sqrt{128x^4y^9} \) is:
\[
8x^2y^4\sqrt{2y}
\]

Based on the provided options, none precisely matches this exact expression, but we can see that it simplifies consistently. If you have a specific option in mind and want a detailed check against it, feel free to point it out!