Final answer:
To solve the equation 5l = 69120 l⁴ / 13824², we can simplify it by canceling out common factors and then rearrange the equation to solve for l. The equation has four possible solutions: l = 0, l = 1, l = -1, and l = -4.
Step-by-step explanation:
To solve the equation 5l = 69120 l⁴ / 13824², we can simplify it by canceling out common factors. First, divide both sides of the equation by 13824²: l = (69120 l⁴) / (13824² * 5). Next, simplify the equation further: l = l⁴ / 4. Rearranging the equation, we get 4l = l⁴. Now, we can solve for l by taking the fourth root of both sides of the equation: l = (4l)^(1/4). This equation has four possible solutions: l = 0, l = 1, l = -1, and l = -4.