Simplify expressions with zero and negative exponents worksheet.

I'll solve each problem step by step, simplifying the expressions to contain only positive exponents.

Key rules to remember:
- Any number raised to the power of 0 equals 1 (except 0⁰ which is undefined)
- A negative exponent means: a⁻ = 1/aⁿ
- When you have multiple variables with exponents, handle each one separately

Let me work through each problem:

Problem 1: 2⁰
Any non-zero number to the power of 0 equals 1.
Answer: 1

Problem 2: 2⁻¹
Negative exponent means take the reciprocal: 2⁻¹ = 1/2¹ = 1/2
Answer: 1/2

Problem 3: (-2)⁻¹
The negative sign is inside the parentheses, so it's part of the base: (-2)⁻¹ = 1/(-2)¹ = -1/2
Answer: -1/2

Problem 4: (-5)⁻¹
Similarly: (-5)⁻¹ = 1/(-5)¹ = -1/5
Answer: -1/5

Problem 5: (9s)⁻²
Apply the exponent to both parts: (9s)⁻² = 1/(9s)² = 1/(81s²)
Answer: 1/(81s²)

Problem 6: 2u⁰v⁻³
u⁰ = 1, and v⁻³ = 1/v³
So: 2 × 1 × (1/v³) = 2/v³
Answer: 2/v³

Problem 7: 2p⁻¹q
p⁻¹ = 1/p, and q⁰ = 1
So: 2 × (1/p) × 1 = 2/p
Answer: 2/p

Problem 8: 3a⁻³b⁰
a⁻³ = 1/a³, and b⁰ = 1
So: 3 × (1/a³) × 1 = 3/a³
Answer: 3/a³

Problem 9: a⁻⁴b⁻⁴
Both have negative exponents: a⁻⁴ = 1/a⁴ and b⁻⁴ = 1/b⁴
So: (1/a⁴) × (1/b⁴) = 1/(a⁴b⁴)
Answer: 1/(a⁴b⁴)

Problem 10: a⁻⁴b²
Only a has a negative exponent: a⁻⁴ = 1/a⁴
So: (1/a⁴) × b² = b²/a⁴
Answer: b²/a⁴

Problem 11: 2u⁻¹v⁻¹
Both u and v have negative exponents: u⁻¹ = 1/u and v⁻¹ = 1/v
So: 2 × (1/u) × (1/v) = 2/(uv)
Answer: 2/(uv)

Problem 12: 2x⁻¹b⁰
x⁻¹ = 1/x, and b⁰ = 1
So: 2 × (1/x) × 1 = 2/x
Answer: 2/x

Final Answer:
1. 1
2. 1/2
3. -1/2
4. -1/5
5. 1/(81s²)
6. 2/v³
7. 2/p
8. 3/a³
9. 1/(a⁴b⁴)
10. b²/a⁴
11. 2/(uv)
12. 2/x