Let's solve the expression \(\frac{16^4}{4^6}\).

1. First, express 16 and 4 in terms of powers of 2:
   \[
   16 = 2^4 \quad \text{and} \quad 4 = 2^2
   \]
   So, the expression becomes:
   \[
   \frac{(2^4)^4}{(2^2)^6}
   \]

2. Simplify the exponents:
   \[
   \frac{2^{4 \times 4}}{2^{2 \times 6}} = \frac{2^{16}}{2^{12}}
   \]

3. Apply the property of exponents \(\frac{a^m}{a^n} = a^{m-n}\):
   \[
   2^{16-12} = 2^4
   \]

4. Simplify further:
   \[
   2^4 = 16
   \]

So, the final answer is \(16\).

Would you like a more detailed explanation or have any other questions?

Here are 5 related questions:
1. What is the result of \(\frac{32^3}{8^5}\)?
2. How do you simplify \(\frac{25^2}{5^6}\)?
3. What is \(4^{\frac{3}{2}}\) in simplified form?
4. How do you calculate \(\frac{64^2}{4^5}\)?
5. How do you simplify expressions with fractional exponents?

**Tip:** When working with exponents, always look for opportunities to factor numbers into smaller bases for easier simplification!

Learn how to solve the mathematical expression (16^4 / 4^6) step-by-step with a detailed explanation. This problem involves exponentiation and the application of exponent rules. Suitable for students in Grades 7-9.

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