https://r2.erweima.ai/mathbot/image/1726349967745v68vtd19.jpg

The expression in the image is:

\[
\frac{2^4}{2^{-2}}
\]

### Step-by-step Solution:

1. **Simplify the exponents:**
   Using the rule of exponents \(\frac{a^m}{a^n} = a^{m-n}\), we can combine the terms in the numerator and denominator:
   \[
   \frac{2^4}{2^{-2}} = 2^{4 - (-2)} = 2^{4 + 2} = 2^6
   \]

2. **Calculate \(2^6\):**
   \[
   2^6 = 64
   \]

So, the simplified expression equals \(64\).

Would you like more details or have any questions?

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Here are five related questions to further explore this topic:

1. What happens if you reverse the exponents in the denominator, such as \(\frac{2^4}{2^2}\)?
2. How would this calculation change if the base were a different number, say \(3\) instead of \(2\)?
3. Can you apply the exponent rule to fractions like \(\frac{3^5}{3^{-1}}\)?
4. What is the general formula for multiplying exponents with the same base?
5. How do negative exponents behave with different bases?

**Tip:** Always remember that a negative exponent means taking the reciprocal of the base raised to the positive exponent. For example, \(a^{-n} = \frac{1}{a^n}\).

Learn how to simplify the expression 2^4 divided by 2^(-2) by applying exponent rules. This problem demonstrates how to handle negative exponents and simplify expressions using the properties of exponents. Suitable for students in Grades 7-9.

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