Exponent Calculator – Powers & Indices

Quy tắc số mũ

Exponents represent repeated multiplication: a^n = a × a × ... × a (n times). Key rules:

• Product: a^m × a^n = a^(m+n)
• Quotient: a^m / a^n = a^(m−n)
• Power of a power: (a^m)^n = a^(m×n)
• Zero exponent: a^0 = 1 (for any a not equal to 0)
• Negative exponent: a^(−n) = 1/a^n
• Fractional exponent: a^(1/n) = nth root of a

Số lớn và ký hiệu khoa học

Exponents make large and small numbers manageable. The observable universe is about 8.8 × 10^26 meters across. A hydrogen atom is about 1.2 × 10^(−10) meters. Without exponents, these numbers would be impossibly long to write.

Common powers of 2: 2^10 = 1,024 (≈1 thousand, basis of KB). 2^20 = 1,048,576 (≈1 million, MB). 2^30 ≈ 1 billion (GB). 2^40 ≈ 1 trillion (TB).

Tăng trưởng theo cấp số nhân

Exponential growth means a quantity multiplies by a constant factor in each time period. Examples: population growth, compound interest, viral spread, Moore's Law (transistor count doubling every ~2 years).

The key insight: exponential growth starts slow then becomes explosive. Doubling a penny daily for 30 days gives $5.37 million on day 30. Day 20 was only $5,243. Most of the growth happens in the final few doublings.