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The problem asks us to compute the value of \( 4^{\frac{1}{2}} \div 6^{-2} \).

We will solve this step by step:

1. **Evaluate \( 4^{\frac{1}{2}} \)**:  
   The exponent \( \frac{1}{2} \) is equivalent to taking the square root of 4. So:
   \[
   4^{\frac{1}{2}} = \sqrt{4} = 2
   \]

2. **Evaluate \( 6^{-2} \)**:  
   The negative exponent indicates the reciprocal of \( 6^2 \). So:
   \[
   6^{-2} = \frac{1}{6^2} = \frac{1}{36}
   \]

3. **Division of powers**:  
   Now, divide the results:
   \[
   2 \div \frac{1}{36} = 2 \times 36 = 72
   \]

Therefore, the value of the expression is \( 72 \).

Let me know if you would like more details on any step or have any questions! 

### Related Questions:
1. How do you simplify expressions with fractional exponents?
2. What is the rule for negative exponents?
3. Can fractional exponents be negative? How do you handle that?
4. What are the properties of exponents when dividing two numbers?
5. How would the solution change if the bases were different?

### Tip:
When dividing by a fraction, remember that it is the same as multiplying by its reciprocal!

Work out the value of 4^(1/2) ÷ 6^(-2). Give your answer as a whole number or as a fraction in its simplest form.

Find out how to solve the expression 4^(1/2) ÷ 6^(-2) with a detailed, step-by-step solution. This problem involves concepts like fractional exponents, negative exponents, and division of powers, making it suitable for students in Grades 8-10.

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