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The image contains a question from a calculus or algebra assignment. The problem asks to evaluate the expression \( \frac{128}{2^{7/2}} \) using the fact that \( 2^{1/2} = 1.414 \), without using a calculator.

### Step-by-step solution:
1. Break down the exponent in the denominator:
   \[
   2^{7/2} = 2^{3 + 1/2} = 2^3 \times 2^{1/2}
   \]
   We know that \( 2^3 = 8 \) and \( 2^{1/2} = 1.414 \). Therefore:
   \[
   2^{7/2} = 8 \times 1.414 = 11.312
   \]

2. Now, divide the numerator by the result:
   \[
   \frac{128}{2^{7/2}} = \frac{128}{11.312} \approx 11.31
   \]

Thus, the approximate value of the expression is **11.31**.

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### 5 Related Questions:
1. How do you simplify expressions involving fractional exponents?
2. What are the common methods to approximate square roots without a calculator?
3. How can you break down complex powers of 2 into simpler components?
4. How do you handle expressions with mixed operations, like exponents and division?
5. What are common mistakes to avoid when working with fractional exponents?

### Tip:
When dealing with exponents, try to express them in terms of smaller, easily calculable components to simplify your work.

Use the fact that 2^(1/2) = 1.414 to evaluate the following expression without using a calculator: 128 / 2^(7/2).

Learn how to evaluate the expression 128 / 2^(7/2) using exponent rules and approximation techniques. This problem involves algebraic manipulation of fractional exponents and approximation of square roots. Suitable for students in Grades 10-12.

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