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Let's go over the first few problems from the worksheet on "Powers of Monomials." I'll explain the steps to solve each one based on the rules provided.

### Rules Recap:
1. **Power of a Power**: \((a^m)^n = a^{m \cdot n}\)
2. **Power of a Product**: \((a \cdot b)^m = a^m \cdot b^m\)
3. **Power of a Quotient**: \(\left(\frac{a}{b}\right)^m = \frac{a^m}{b^m}\), where \(b \neq 0\)

### Example Problems:
1. **\((x^2)^4\)**
   - Apply the power of a power rule: \(x^{2 \cdot 4} = x^8\)

2. **\((2/3)^2\)**
   - Apply the power of a quotient: \(\frac{2^2}{3^2} = \frac{4}{9}\)

3. **\((y^5)^3\)**
   - Apply the power of a power: \(y^{5 \cdot 3} = y^{15}\)

4. **\((x y)^2\)**
   - Apply the power of a product: \(x^2 \cdot y^2\)

5. **\((3/x)^3\)**
   - Apply the power of a quotient: \(\frac{3^3}{x^3} = \frac{27}{x^3}\)

Would you like help with the remaining problems or any specific explanations? 

Here are five follow-up questions to practice:
1. What happens when you raise a negative base to an odd power?
2. How do you handle exponents when multiplying two terms with the same base?
3. How would you simplify \((2x^3 y)^2\)?
4. What is the result of \(\left(\frac{x^2}{y^3}\right)^4\)?
5. How can the power of a quotient rule help simplify complex fractions?

### Tip:
When simplifying expressions with exponents, always keep track of the sign of the base (positive or negative) to avoid mistakes!

How do you solve problems involving powers of monomials using the power of a power, product, and quotient rules?

Learn how to solve powers of monomials using the power of a power, product, and quotient rules with step-by-step examples. This lesson covers essential algebraic concepts and is suitable for students in Grades 7-9.

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