To solve the equation:

$8x^{\frac{5}{3}} - 24 = 0$

Step 1: Isolate the term with $x$

Add 24 to both sides:

$8x^{\frac{5}{3}} = 24$

Step 2: Divide by 8

Divide both sides of the equation by 8:

$x^{\frac{5}{3}} = \frac{24}{8} = 3$

Step 3: Raise both sides to the power of $\frac{3}{5}$

To eliminate the fractional exponent, raise both sides to the power of $\frac{3}{5}$:

$x = 3^{\frac{3}{5}}$

This is the exact solution.

To express $3^{\frac{3}{5}}$ as a decimal:

$x \approx 1.933$

So, the solution is approximately:

$x \approx 1.933$

Would you like further details or have any questions?

Here are some related questions to explore:

1. How do you solve equations with other fractional exponents?
2. What is the difference between rational and irrational exponents?
3. How do you graph functions involving fractional exponents?
4. How do you simplify expressions with fractional powers?
5. How does raising both sides of an equation to a power affect the solution?

Tip: When solving equations with fractional exponents, always check if you need to raise both sides to the reciprocal power to simplify.