Power Principles

Exponents pack repeated multiplication into shorthand:

• Squaring (n²) gives areas; cubing (n³) gives volumes
• Any number to the zeroth power equals 1, because removing all factors leaves the multiplicative identity
• Negative exponents flip the base: 2^(-3) = 1/8
• Multiplying powers with the same base: add exponents (a^m x a^n = a^(m+n))
• Power of a power: multiply exponents ((a^m)^n = a^(mn))

These five rules handle every exponent problem you will encounter. Archimedes used powers to estimate grains of sand that would fill the universe — arriving at roughly 10^63 — proving that exponents tame even cosmic quantities.