<p>x^10=5555 and x^9/y=5 so what is (x)(y) equal? </p>
<p>I am not quite sure how to come to the answer here, any help please thanks!</p>
<p>This is a tricky problem with a really nice solution behind it, if you approach it from the right angle.</p>
<p>The long way, if you don’t see the trick, is to solve for x in the first equation (it will be the tenth root of 5555, or 5555^(1/10)), then substitute this value in for x in the second equation and solve for y (x^9/y = 5 can be rearranged to x^9/5 = y, or y = 5555^(9/10)/5). Multiply the two values together: 5555^(9/10)/5 * 5555^(1/10) = 5555/5 = 1111.</p>
<p>The trick to avoid all that work, though, depends on a bit of algebra. First, multiply both sides of the second equation by y, so you have x^9 = 5y. Then, multiply both sides of this equation by x; this will give you x^10 = 5xy. Now you have an x^10 term, and you already know what x^10 is because of the first equation; thus, you can substitute the first equation in to get 5555 = 5xy. Divide both sides by 5 to get 1111 = xy, and you now have the answer without having to deal with solving for the exact numerical values of x and y individually.</p>
<p>Awesome! That is great help, I am pondering this question like Aristotle but indeed I am just an hollow man ha, ha…HA!</p>