Simplify the radical expression. (1 point) Responses Image with alt text: Start Fraction 8 lower x superscript 7 baseline lower y superscript 4 baseline Start Root lower x lower y End Root over Start Root 7 lower x lower y superscript 11 baseline End Fraction Image with alt text: Start Fraction 3 lower x superscript 7 baseline over y End Fraction Image with alt text: Start Fraction 9 lower x superscript 7 baseline over lower y End Fraction
To simplify the radical expression, we need to simplify each term under the radical separately.
The first term under the radical is \(8x^7y^4\). We can split this term into two separate radicals: \(\sqrt{x^7y^4} = \sqrt{x^6}\sqrt{xy^4} = x^3y^2\sqrt{xy^4}\).
The entire expression then becomes \(\sqrt{x^3y^2\sqrt{xy^4}}\).
Next, we simplify the second term under the radical which is \(\frac{3x^7}{y}\). We can write it as \(\frac{3x^6}{y} \cdot x\).
Now, the expression becomes \(\sqrt{x^3y^2\sqrt{xy^4}} \cdot \frac{3x^6}{y} \cdot x\).
Finally, we can simplify this further by combining like terms and rearranging the expression as desired.