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The image shows a mathematical expression that involves fractional exponents. The expression is:

\[
4^{\frac{1}{3}} \times 50^{\frac{2}{3}} \times 10^{\frac{5}{3}}
\]

### Step-by-step Solution:

1. **Rewrite the terms with fractional exponents**:
   The general rule for fractional exponents is:  
   \( a^{\frac{m}{n}} = \sqrt[n]{a^m} \).
   Thus, each term becomes:
   
   - \( 4^{\frac{1}{3}} = \sqrt[3]{4} \)
   - \( 50^{\frac{2}{3}} = \sqrt[3]{50^2} = \sqrt[3]{2500} \)
   - \( 10^{\frac{5}{3}} = \sqrt[3]{10^5} = \sqrt[3]{100000} \)

2. **Approximate cube roots**:
   Using approximations for cube roots:
   
   - \( \sqrt[3]{4} \approx 1.587 \)
   - \( \sqrt[3]{2500} \approx 13.643 \)
   - \( \sqrt[3]{100000} \approx 46.416 \)

3. **Multiply the values**:
   Now multiply these approximate values together:
   
   \[
   1.587 \times 13.643 \times 46.416 \approx 1004.79
   \]

So, the approximate value of the expression is:

\[
\boxed{1004.79}
\]

Would you like more details or have any specific questions about this? Here are some follow-up questions that might interest you:

1. How do you calculate cube roots for larger numbers more precisely?
2. What is the difference between fractional exponents and radicals?
3. Can you explain how to multiply terms with exponents?
4. How would this problem change if one of the exponents were negative?
5. Can the result of this expression be expressed in a simpler form?

**Tip:** To improve accuracy, use a scientific calculator or tools for cube roots and more complex calculations.

Calculate the value of the expression: 4^(1/3) * 50^(2/3) * 10^(5/3).

Learn how to calculate the value of the expression 4^(1/3) * 50^(2/3) * 10^(5/3) with a detailed step-by-step solution. This problem covers key mathematical concepts such as exponents, radicals, and multiplication, suitable for students in Grades 10-12.

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