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Answer:
1. 5² × 5³ = 5⁵ = 3125
2. 5² ÷ 5³ = 1/5¹ = 1/5
3. 2⁻² = 1/2² = 1/4
4. 1⁶ - 2⁶ + 5⁰ = 1⁷ = 1
5. 2³ × 3⁰ = 8 × 1 = 8
6. 2² × 3² = 6² = 36
7. a² × b² = ab²
Step-by-step explanation:
1. 5² × 5³ = 5 ²⁺³ (mᵃ × mᵇ = mᵃ⁺ᵇ)
= 5⁵ = 3125
2. 5² ÷ 5³ = 5²⁻³ (mᵃ ÷ mᵇ = mᵃ⁻ᵇ)
= 5⁻¹ (m⁻ᵃ = 1/mᵃ)
= 1/5¹ = 1/5
3. 2⁻² = 1/2² (m⁻ᵃ = 1/mᵃ)
= 1/4
4. 1⁶ - 2⁶ + 5⁰ = (1⁶ - 2⁶) + 5⁰ (mᵃ - nᵃ = m-nᵃ)
= 1⁶ + 5⁰ (a⁰ = 1)
= 1⁶ + 1
= 1⁷ = 1
5. 2³ × 3⁰ = 2³ × 1 (a⁰ = 1)
= 8 × 1 = 8
6. 2² × 3² = (2×3)² [mᵃ×nᵃ = (m×n)ᵃ]
= 6² = 36
7. a² × b² = (a × b)² [mᵃ×nᵃ = (m×n)ᵃ]
= ab²
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