https://file.aiquickdraw.com/mathbot/file/1726791699210mpevxr6p.jpg

Let's solve each problem from the image one by one:

### 1. Problem:
\[
\left(\frac{1}{P^2q^4r} \div \frac{1}{4p q^4}\right)^8
\]

First, simplify the expression inside the parentheses:
\[
\frac{1}{P^2q^4r} \div \frac{1}{4pq^4} = \frac{1}{P^2q^4r} \times \frac{4pq^4}{1} = \frac{4pq^4}{P^2q^4r} = \frac{4p}{P^2r}
\]

Now, we apply the exponent 8 to each part:
\[
\left(\frac{4p}{P^2r}\right)^8 = \frac{(4p)^8}{(P^2r)^8} = \frac{4^8 \cdot p^8}{P^{16} \cdot r^8}
\]

Thus, the result for the first problem is:
\[
\frac{4^8 \cdot p^8}{P^{16} \cdot r^8}
\]

### 2. Problem:
\[
\frac{(3m)^5 \times \left((3m)^{-1}\right)^2}{(3m)^4 \div (3m)^3}
\]

Start simplifying each part:
\[
(3m)^5 = 3^5m^5, \quad \left((3m)^{-1}\right)^2 = (3m)^{-2}, \quad (3m)^4 = 3^4m^4, \quad \text{and} \quad (3m)^3 = 3^3m^3
\]

The expression becomes:
\[
\frac{3^5m^5 \times 3^{-2}m^{-2}}{3^4m^4 \div 3^3m^3} = \frac{3^5m^5 \times 3^{-2}m^{-2}}{3^1m^1}
\]

Simplify the powers:
\[
= \frac{3^{5-2}m^{5-2}}{3^1m^1} = \frac{3^3m^3}{3^1m^1} = 3^{3-1}m^{3-1} = 3^2m^2
\]

Thus, the result is:
\[
9m^2
\]

### 3. Problem:
Price of 2 kg of sugar is Rp. 26,500. The price of 20 kg is:
\[
\text{Price of 20 kg} = \frac{20}{2} \times 26,500 = 10 \times 26,500 = 265,000
\]

Thus, the price for 20 kg of sugar is **Rp. 265,000**.

### 4. Problem:
Find the value of \(B^8 \times B^0\).

Since \(B^0 = 1\), the expression becomes:
\[
B^8 \times 1 = B^8
\]

Thus, the value is:
\[
B^8
\]

### 5. Problem:
Simplify to positive exponents: \((2k^4l)^{-2}\)

Apply the negative exponent:
\[
(2k^4l)^{-2} = \frac{1}{(2k^4l)^2} = \frac{1}{2^2k^8l^2} = \frac{1}{4k^8l^2}
\]

Thus, the simplified form is:
\[
\frac{1}{4k^8l^2}
\]

---

Would you like to proceed with solving more of these, or do you have questions about any of the steps? 

Here are 5 related questions to expand your knowledge:
1. How do you handle exponents when multiplying terms with the same base?
2. How would you approach dividing terms with exponents?
3. What is the general rule for handling negative exponents?
4. How would you simplify expressions involving fractions and exponents together?
5. What is the significance of a base raised to the power of zero?

**Tip**: Always combine like terms with the same base when simplifying exponential expressions.

Learn how to simplify expressions involving exponents and negative powers with a detailed step-by-step solution. This problem covers key algebraic concepts, including the laws of exponents and their application in simplifying complex expressions. Suitable for students in Grades 8-10.

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