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jawab soal matematika no 5 menggunakan cara

We are asked to simplify the given mathematical expression:

\[
\frac{2^5 \times 16 \times 2^{-4}}{4 \times 2^5 \times 32}
\]

### Step 1: Rewrite the constants as powers of 2
- \( 16 = 2^4 \)
- \( 4 = 2^2 \)
- \( 32 = 2^5 \)

So the expression becomes:
\[
\frac{2^5 \times 2^4 \times 2^{-4}}{2^2 \times 2^5 \times 2^5}
\]

### Step 2: Combine powers of 2 using the rule \( a^m \times a^n = a^{m+n} \)
In the numerator:
\[
2^5 \times 2^4 \times 2^{-4} = 2^{5 + 4 - 4} = 2^5
\]

In the denominator:
\[
2^2 \times 2^5 \times 2^5 = 2^{2 + 5 + 5} = 2^{12}
\]

Now the expression becomes:
\[
\frac{2^5}{2^{12}}
\]

### Step 3: Simplify the powers of 2 using the rule \( \frac{a^m}{a^n} = a^{m-n} \)
\[
\frac{2^5}{2^{12}} = 2^{5 - 12} = 2^{-7}
\]

### Step 4: Convert the negative exponent to a fraction
\[
2^{-7} = \frac{1}{2^7} = \frac{1}{128}
\]

### Final Answer:
The simplified form of the given expression is:
\[
\frac{1}{128}
\]

Would you like further explanation on any step?

---

Here are 5 related questions for practice:
1. Simplify \( \frac{3^4 \times 9}{27} \).
2. Simplify \( \frac{5^3 \times 25}{5^5} \).
3. Simplify \( \frac{2^6 \times 8}{16 \times 4} \).
4. Simplify \( \frac{3^2 \times 81}{9^2} \).
5. Simplify \( \frac{2^4 \times 32}{16 \times 2^2} \).

**Tip:** When simplifying exponents, always try to express constants as powers of the same base to make calculations easier.

Sederhanakanlah bentuk \( \frac{2^5 \times 16 \times 2^{-4}}{4 \times 2^5 \times 32} \)

Learn how to simplify exponent expressions like \( \frac{2^5 \times 16 \times 2^{-4}}{4 \times 2^5 \times 32} \) by applying the laws of exponents. This solution includes step-by-step instructions and key exponent rules, suitable for students in Grades 9-11.

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