Let's solve \(\frac{4^4 \times 2^2}{16^3}\) step by step.

### Step 1: Simplify the powers of each base.
- \(4^4 = (2^2)^4 = 2^8\)
- \(2^2 = 4\)
- \(16 = 2^4\), so \(16^3 = (2^4)^3 = 2^{12}\)

### Step 2: Substitute the simplified terms into the original expression:
\[
\frac{4^4 \times 2^2}{16^3} = \frac{2^8 \times 2^2}{2^{12}}
\]

### Step 3: Combine the exponents in the numerator.
Using the rule \(a^m \times a^n = a^{m+n}\):
\[
2^8 \times 2^2 = 2^{10}
\]

So the expression becomes:
\[
\frac{2^{10}}{2^{12}}
\]

### Step 4: Subtract the exponents in the fraction.
Using the rule \(\frac{a^m}{a^n} = a^{m-n}\):
\[
2^{10 - 12} = 2^{-2}
\]

### Step 5: Simplify the result.
\[
2^{-2} = \frac{1}{2^2} = \frac{1}{4}
\]

### Final Answer:
\[
\frac{4^4 \times 2^2}{16^3} = \frac{1}{4}
\]

Let me know if you need further clarification or details!

Here are some related questions for practice:
1. What is \( \frac{3^5 \times 9^2}{27^3} \)?
2. Simplify \( 5^3 \times 25^2 \).
3. How do you simplify \( \frac{2^6 \times 4^3}{8^2} \)?
4. Evaluate \( \frac{6^4}{36^2} \).
5. Simplify \( \frac{2^3 \times 2^5}{2^7} \).

**Tip:** When multiplying or dividing powers with the same base, remember to add or subtract the exponents!

Discover how to simplify the expression (4⁴*2²) ÷ 16³ by applying the laws of exponents. This problem demonstrates key exponent rules, including multiplication and division of powers, and is suitable for students in Grades 8-10.

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