$\frac{(x^8)^4 * (x^5)^9}{(x^{15})^4 * (x^4)^4} = 5$
$\frac{x^{8 * 4 + 5 * 9}}{x^{15 * 4 + 4 * 4}} = 5$
$\frac{x^{32 + 45}}{x^{60 + 16}} = 5$
$\frac{x^{77}}{x^{76}} = 5$
$x^{77 - 76} = 5$
$x^{1} = 5$
$x^{1} = 5^1$
x = 5

$\frac{x^{17} * x^{23}}{(x^{8})^3 * x^5 * (x^2)^3} = -243$
$\frac{x^{17 + 23}}{x^{8 * 3 + 5 + 2 * 3}} = -243$
$\frac{x^{40}}{x^{24 + 5 + 6}} = -243$
$\frac{x^{40}}{x^{35}} = -243$
$x^{40 - 35} = -243$
$x^{5} = -243$
$x^{5} = (-3)^5$
x = −3

$\frac{(x^{45})^2 : (x^{40})^2}{(x^{5})^4 : x^{17}} = -1$
$\frac{x^{45 * 2 - 40 * 2}}{x^{5 * 4 - 17}} = -1$
$\frac{x^{90 - 80}}{x^{20 - 17}} = -1$
$\frac{x^{10}}{x^{3}} = -1$
$x^{10 - 3} = -1$
$x^{7} = -1$
$x^{7} = (-1)^7$
x = −1

$\frac{(x^{5})^2 * (x^{4})^7 * x}{x^{130} : (x^{25})^4} = 512$
$\frac{x^{5 * 2 + 4 * 7 + 1}}{x^{130 - 25 * 4}} = 512$
$\frac{x^{10 + 28 + 1}}{x^{130 - 100}} = 512$
$\frac{x^{39}}{x^{30}} = 512$
$x^{39 - 30} = 512$
$x^{9} = 512$
$x^{9} = 2^9$
x = 2