Exponent Rules (A) worksheet with 10 problems to simplify expressions.

I'll solve each exponent problem step by step, applying the appropriate exponent rules.

Let me work through all 10 problems:

Problem 1: (7⁴)⁸
- Rule: When raising a power to another power, multiply the exponents
- (7⁴) = 7^(4×8) = 7³²

Problem 2: 3⁷ · 3⁷
- Rule: When multiplying with same base, add the exponents
- 3⁷ · 3⁷ = 3^(7+7) = 3¹

Problem 3: 4³/4³
- Rule: When dividing with same base, subtract the exponents
- 4³/4³ = 4^(3-3) = 4 = 1

Problem 4: 2⁶ · 2⁵
- Rule: When multiplying with same base, add the exponents
- 2⁶ · 2⁵ = 2^(6+5) = 2¹¹

Problem 5: 5³/5⁸
- Rule: When dividing with same base, subtract the exponents
- 5³/5⁸ = 5^(3-8) = 5⁵ = 1/5⁵

Problem 6: 5⁷ · 8
- Rule: When multiplying with same exponent but different bases, combine the bases
- 5⁷ · 8⁷ = (5·8)⁷ = 40⁷

Problem 7: (2⁴)⁵
- Rule: When raising a power to another power, multiply the exponents
- (2⁴)⁵ = 2^(4×5) = 2²⁰

Problem 8: 7⁸/7²
- Rule: When dividing with same base, subtract the exponents
- 7⁸/7² = 7^(8-2) = 7⁶

Problem 9: 6⁸ · 6⁰
- Rule: When multiplying with same base, add the exponents; also, any number to the 0 power equals 1
- 6⁸ · 6⁰ = 6^(8+0) = 6⁸ · 1 = 6⁸

Problem 10: 3⁵/3⁵
- Rule: When dividing with same base, subtract the exponents
- 3⁵/3⁵ = 3^(5-5) = 3⁰ = 1

Final Answer:
1. 7³²
2. 3¹⁴
3. 1
4. 2¹¹
5. 1/5⁵ or 5⁻⁵
6. 40⁷
7. 2²⁰
8. 7⁶
9. 6⁸
10. 1