https://file.aiquickdraw.com/mathbot/file/17270898692129y2j9j7z.jpg

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.

(25)^{1/2} + (36)^{1/2} - (27)^{1/3} divided by (125)^{2/3}

Learn how to simplify expressions with fractional exponents using roots and powers. This example involves square and cube roots and covers key concepts such as properties of exponents and simplifying radicals. Suitable for students in Grades 9-11.

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