Exponent / Power Calculator

Pro tips most people learn the hard way

• The Rule of 72 is the most useful exponent shortcut for everyday finance. To estimate doubling time at any constant growth rate, divide 72 by the rate. Your money at 6 percent doubles in 12 years (72/6); at 9 percent in 8 years (72/9). It's an approximation of ln(2)/ln(1+r) but accurate enough for mental math.
• Powers of 2 deserve memorization for anyone in tech. 2^10 = 1024 (KiB), 2^20 ≈ 1.05 million (MiB), 2^30 ≈ 1.07 billion (GiB), 2^32 ≈ 4.3 billion (the old IPv4 address space limit). Spotting 'this is a power-of-2 boundary' is half of low-level debugging.
• Negative exponents are just reciprocals — once that clicks, they stop being scary. 2^(−3) is 1/2^3 = 1/8. Fractional exponents are roots — 8^(1/3) is the cube root of 8, which is 2. Both follow from the same exponent laws as integer exponents; nothing new is happening, just consistent extension.
• Exponential growth defeats linear intuition. Pandemic spread, compound interest, viral content, Moore's Law on chip transistors — all exponential. If something doubles every period, after 10 periods you have 1024× the original, after 20 you have over a million times. This is why catching exponential trends early matters far more than reacting to them later.
• Honest take: 0^0 is one of math's edge cases. Combinatorics and algebra define it as 1 because that keeps formulas clean (especially the binomial theorem). Analysis sometimes leaves it undefined because the limit depends on the path taken. Pick whichever convention your context demands — but be aware the choice exists.