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The worksheet is titled "Rewriting Using the Laws of Exponents," and the problems listed require applying exponent rules such as the product of powers, power of a power, and other exponent properties.

I will provide the solutions for the first few problems as examples:

1. \( 3^0 = 1 \) (Any number raised to the power of 0 is 1).
2. \( 3^3 \times 3^5 = 3^{3+5} = 3^8 \) (When multiplying powers with the same base, add the exponents).
3. \( \left( \frac{1}{7} \right)^3 = \frac{1^3}{7^3} = \frac{1}{343} \).
4. \( (7 \times 2)^2 = 7^2 \times 2^2 = 49 \times 4 = 196 \).
5. \( (8 \times 3)^9 = 8^9 \times 3^9 \).

Would you like the solutions to the remaining problems, or do you want further details on any of these answers? Let me know if you'd like to focus on any specific rule of exponents.

Here are five related questions to expand your knowledge:
1. How do you apply the power of a product rule in exponentiation?
2. What is the general rule for multiplying numbers with the same base and different exponents?
3. How does the zero exponent rule work for negative numbers?
4. What happens when you raise a fraction to a power?
5. How can the distributive property be applied in exponent problems involving both addition and multiplication?

**Tip:** When dealing with negative exponents, remember that \( a^{-n} = \frac{1}{a^n} \).

Math worksheet titled 'Rewriting Using the Laws of Exponents' with problems related to exponent rules, such as simplifying expressions using the product of powers, power of a power, and other properties of exponents.

Practice simplifying expressions using exponent laws in this worksheet. Topics include the zero exponent rule, product of powers, power of a power, and power of a product rule. Suitable for students in Grades 7-9.

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