Power Play

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Exponential notation is a way to write repeated multiplication using a base and exponent. 5⁴ means 5 × 5 × 5 × 5 = 625. It is read as '5 raised to the power 4' or '5 to the power 4' or 'the 4th power …

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3⁷ (3 raised to the power 7). Here, 3 is the base and 7 is the exponent, meaning 3 is multiplied by itself 7 times.

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When multiplying powers with the same base, add the exponents: nᵃ × nᵇ = nᵃ⁺ᵇ. Example: 2³ × 2⁵ = 2³⁺⁵ = 2⁸ = 256.

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When dividing powers with the same base, subtract the exponents: nᵃ ÷ nᵇ = nᵃ⁻ᵇ (where n ≠ 0). Example: 7⁶ ÷ 7² = 7⁶⁻² = 7⁴ = 2401.

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When raising a power to another power, multiply the exponents: (nᵃ)ᵇ = nᵃˣᵇ. Example: (3²)⁴ = 3²ˣ⁴ = 3⁸ = 6561.

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Any non-zero number raised to the power 0 equals 1. This is because n⁰ = nᵃ⁻ᵃ = nᵃ ÷ nᵃ = 1 for any value of a. Example: 5⁰ = 1, (-3)⁰ = 1.

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A negative exponent means taking the reciprocal of the positive power: n⁻ᵃ = 1/nᵃ. So 2⁻³ = 1/2³ = 1/8 = 0.125.

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32400 = 2⁴ × 3⁴ × 5². Breaking it down: 32400 = 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 5 × 5 = 2⁴ × 3⁴ × 5².