Question 1168255
your equation is 8x^3/x^5 = 512


since x^3 / x^5 is equal to 1/x^2, the equation becomes:


8/x^2 = 512


multiply both sides of the equation by x^2 and divide both sides of the equation by 512 to get:


8/512 = x^2


simplify to get:


1/64 = x^2


solve for x to get:


x = plus or minus (1/8)


those are your solutions.


x = 1/8 or x = -1/8 (correction to previous answer was made here.


if you graphed the equation of y = 8x^3/x^5 and graphed the equation of x = -1/8 and x = 1/8, and then took the intersection of the first equation with the last two, it would look like this.


<img src = "http://theo.x10hosting.com/2020/102601.jpg" >


you can see that the intersection points of the first equation with the second and third equation is at y = 512.


the graph shows the x values of the coordinate points as plus or minus .0125


plus or minus .0125 is equal to plus or minus 1/8.


you can also see from the graph, that the equation of y = 8x^3/x^5 has a vertical asymptote at x = 0.


that's because the equation is undefined at x = 0 because it becomes 0/0.


as the value of x approaches 0 from either to the left of it or to the right of it, the value of y becomes greater and greater as x gets closer and closer to 0.


as 2 examples, consider x = plus or minus .02 and x = plus or minus .01.


when x = plus or minus .02, the value of y = 20,000.


when x = plus or minus .01, the value of y = 80,000.


one more value of x at .005 should cement the progression.


when x = plus or minus .005, the value of y = 320,000


y will get larger and larger when x approaches 0 from either end.


x can never be 0, hence the vertical asymptote at x = 0