Index laws: cheat sheet

Irrational numbers and index laws · The words and methods from the lessons, with an example of each.

Write the powers out as factors to see why. Only powers of the same base combine.

a^m \times a^n = a^{m+n} \quad a^m \div a^n = a^{m-n} \quad (a^m)^n = a^{mn}

aⁿ ÷ aⁿ = 1, and the quotient law calls it a⁰.

a^0 = 1 \quad (a \ne 0)