You are given the expression \( N(72) = 2^{\frac{72}{3.5}} \). Let's simplify it step by step:

1. First, compute the fraction \( \frac{72}{3.5} \):
   \[
   \frac{72}{3.5} = \frac{72 \times 10}{3.5 \times 10} = \frac{720}{35} = 20.5714
   \]

2. Now substitute this back into the original expression:
   \[
   N(72) = 2^{20.5714}
   \]

3. To approximate the value of \( 2^{20.5714} \), use a calculator:
   \[
   2^{20.5714} \approx 1521384.94
   \]

Thus, \( N(72) \approx 1,521,384.94 \).

Would you like further clarification or details on any of the steps?

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Here are 5 related questions to deepen your understanding:
1. How can you simplify other exponential expressions like \( 2^{\frac{n}{m}} \)?
2. What happens to the value of an expression as the exponent increases for powers of 2?
3. How do you calculate fractional exponents without a calculator?
4. What is the general rule for multiplying exponents with the same base?
5. How can you apply logarithms to solve for exponents?

**Tip:** When dealing with fractional exponents, remember that you can break them down into roots and powers (e.g., \( a^{m/n} = \sqrt[n]{a^m} \)).

Learn how to simplify the exponential expression N(72) = 2^(72/3.5) step-by-step. The solution covers the calculation of fractional exponents and key algebraic concepts. Suitable for students in Grades 8-10.

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