Answer
$x \approx ±6$
Work Step by Step
1. Power equation
For example:
$7^{x} + 3 = 0$ is an exponential equation (The variable is the exponent)
$x^{7} + 3 =0 $ is a power equation (The variable is raised to the power of a number)
2. Solve
$\frac{1}{3}x^{8} - 24 = \frac{5}{3}x^{8} - 2239464$
$\frac{x^{8}}{3} - \frac{5x^{8}}{3} = -2239464 + 24$
$-\frac{4x^{8}}{3} = -2239440$
$\frac{4x^{8}}{3} = 2239440$
$4x^{8} = 6718320$
$x^{8} = 1679580$
$x = ±(1679580)^{\frac{1}{8}}$
$x = ±5.999...$
$x \approx ±6$
Check:
When $x = 6$
$\frac{1}{3}(5.99...)^{8} - 24 \overset{?}{=} \frac{5}{3}(5.99...)^{8} - 2239464$
$\frac{1}{3}(1679580.001) - 24 \overset{?}{=} \frac{5}{3}(1679580.001) - 2239464$
$\frac{1679580.001}{3}- 24 \overset{?}{=} \frac{5(1679580.001)}{3} - 2239464$
$559860.003- 24 \overset{?}{=} 2799300.002 - 2239464$
$559836.003 \approx 559836.0017$
$559,836 \approx 559,836$
When $x = -6$
$\frac{1}{3}(-5.99...)^{8} - 24 \overset{?}{=} \frac{5}{3}(-5.99...)^{8} - 2239464$
$\frac{1}{3}(1679580.001) - 24 \overset{?}{=} \frac{5}{3}(1679580.001) - 2239464$
$\frac{1679580.001}{3}- 24 \overset{?}{=} \frac{5(1679580.001)}{3} - 2239464$
$559860.003- 24 \overset{?}{=} 2799300.002 - 2239464$
$559836.003 \approx 559836.0017$
$559,836 \approx 559,836$
