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Index laws: cheat sheet

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

index laws

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

am×an=am+nam÷an=am−n(am)n=amna^m \times a^n = a^{m+n} \quad a^m \div a^n = a^{m-n} \quad (a^m)^n = a^{mn}
3⁵ ÷ 3²: pairs of 3s cancel
3⁵ ÷ 3²: pairs of 3s cancel

zero index

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

a0=1(a≠0)a^0 = 1 \quad (a \ne 0)