Algebraic Roots and Indices

Negative indices

• A negative index means the reciprocal of the positive power
  • p⁻³ = 1/p³
• The sign of the index says nothing about the sign of the value

Fractional indices

• A unit fraction index is a root, with the denominator giving which root
  • a^(1/2) is the square root and a^(1/3) is the cube root
• A general fraction m/n combines both: take the nth root, then raise to the power m
  • 8^(2/3) is the cube root of 8, which is 2, then squared, giving 4
• Rooting before powering keeps the numbers small, which matters without a calculator
• A negative fractional index combines the two ideas, giving one over the root