Question

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

Answer 1

To simplify the radical expression, we need to simplify each term under the radical separately.

The first term under the radical is $8x^7{y}^4$. We can split this term into two separate radicals: $\sqrt{x^7{y}^4}=\sqrt{x^6}\sqrt{x{y}^4}=x^3{y}^2\sqrt{x{y}^4}$.

The entire expression then becomes $\sqrt{x^3{y}^2\sqrt{x{y}^4}}$.

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 $\sqrt{x^3{y}^2\sqrt{x{y}^4}}\cdot \frac{3x^6}{y}\cdot x$.

Finally, we can simplify this further by combining like terms and rearranging the expression as desired.