Solve the equation. (x^2+24x)^1/4=3 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is 4 square (Simplify your answer. Type an integer er or a fraction. Use a comma to separate answers as needed.) B. The solution set is the empty set.

To solve the equation $(x^{2}+24x)^{1/4}=3$, we need to raise both sides of the equation to the power of 4 to eliminate the fourth root:<br /><br />$(x^{2}+24x)^{1/4} = 3$<br /><br />$(x^{2}+24x) = 3^4$<br /><br />$(x^{2}+24x) = 81$<br /><br />Now, we can solve the quadratic equation $x^{2}+24x-81=0$ by factoring:<br /><br />$(x+27)(x-3) = 0$<br /><br />Setting each factor equal to zero gives us the solutions:<br /><br />$x+27 = 0$ or $x-3 = 0$<br /><br />$x = -27$ or $x = 3$<br /><br />Therefore, the solution set is $\{-27, 3\}$.<br /><br />So, the correct choice is A. The solution set is $\{-27, 3\}$.