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I do not get how to simplify this at all can u help pls im dying rn

Let’s simplify the given expression step by step. The expression is:

\[
\frac{3^2 \cdot (2^2)^{-2}}{2^3}
\]

### Step 1: Simplify the powers.
- \( 3^2 = 9 \)
- For \( (2^2)^{-2} \), apply the exponent rule \( (a^m)^n = a^{m \cdot n} \), so:
  \[
  (2^2)^{-2} = 2^{2 \cdot (-2)} = 2^{-4}
  \]

Now, the expression becomes:
\[
\frac{9 \cdot 2^{-4}}{2^3}
\]

### Step 2: Combine the powers of 2.
The next step is to simplify the powers of 2. Use the rule \( a^m \cdot a^n = a^{m+n} \). We need to combine \( 2^{-4} \) and \( 2^3 \).

First, notice that \( 2^{-4} \) and \( 2^3 \) are in division, so apply the rule \( \frac{a^m}{a^n} = a^{m-n} \):

\[
2^{-4} \div 2^3 = 2^{-4-3} = 2^{-7}
\]

So the entire expression simplifies to:
\[
9 \cdot 2^{-7}
\]

### Step 3: Final simplified expression.
Since there are no further simplifications, the final simplified form is:

\[
\frac{9}{2^7}
\]

### Step 4: Optional evaluation.
If you'd like to express it as a decimal or fraction:

\[
2^7 = 128, \quad \text{so} \quad \frac{9}{128}
\]

Thus, the simplified expression is either \( \frac{9}{128} \) or as a decimal approximately \( 0.0703 \).

---

Would you like more details or have any questions? Here are 5 related problems to practice:

1. Simplify \( \frac{4^3 \cdot (3^2)^{-2}}{3^4} \).
2. What is \( \frac{5^2 \cdot (2^3)^{-1}}{2^4} \) simplified?
3. Evaluate \( (7^2)^{-1} \cdot (7^3)^{-2} \).
4. Simplify \( \frac{6^4 \cdot (2^5)^{-3}}{6^2 \cdot 2^{-4}} \).
5. What is the decimal value of \( \frac{7}{2^6} \)?

**Tip:** Always apply the exponent rules first when simplifying expressions with exponents!

Learn how to simplify the expression 3^2 * (2^2)^(-2) / 2^3 using exponent rules. This step-by-step solution explains the application of exponent properties to simplify the expression. Suitable for students in Grades 9-11.

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