The expression given in the image is:

$\frac{(25)^{\frac{1}{2}} + (36)^{\frac{1}{2}} - (27)^{\frac{1}{3}}}{(125)^{\frac{2}{3}}}$

Step-by-step solution:

1. Simplify the terms with fractional exponents:

   • $(25)^{\frac{1}{2}}$ = $\sqrt{25} = 5$
   • $(36)^{\frac{1}{2}}$ = $\sqrt{36} = 6$
   • $(27)^{\frac{1}{3}}$ = $\sqrt[3]{27} = 3$
   • $(125)^{\frac{2}{3}}$ = $\left(\sqrt[3]{125}\right)^2 = 5^2 = 25$

2. Substitute these values back into the expression:

$\frac{5 + 6 - 3}{25}$

3. Simplify the numerator:

$5 + 6 - 3 = 8$

4. Final expression:

$\frac{8}{25}$

So, the value of the entire expression is:

$\boxed{\frac{8}{25}}$

Would you like further details or have any questions about the steps? Here are five related questions to explore:

1. What is the general rule for simplifying expressions with fractional exponents?
2. How do you compute cube roots and square roots of numbers?
3. What is the difference between simplifying a square root and a cube root?
4. How do you convert fractional exponents to radical expressions?
5. Can you explain how fractional exponents affect the base of a number?

Tip:

When simplifying expressions with fractional exponents, remember that $a^{\frac{m}{n}}$ means $\sqrt[n]{a^m}$, which can help break complex expressions into manageable parts.