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Laws of indices - AQALetters or numbers to the power of zero

Laws of indices give rules for simplifying calculations or expressions involving powers of the same base.

Part ofMathsNumber

Letters or numbers to the power of zero

Click to explore updated revision resources for GCSE Maths:The power of zero, with step-by-step slideshows, quizzes, practice exam questions, and more!

This can be seen in the example of \(j^2 \div j^2\).

Subtract the powers, so \(j^2 \div j^2 = j^{2 - 2} = j^0\).

Any number or letter divided by itself is 1.

This gives \(j^2 \div j^2 = j^0\) (using index laws for division) and \(j^2 \div j^2 = 1\), which means \(j^0 = 1\).

Laws of indices - summary

  • \(a^m \times a^n = a^{m + n}\)
  • \(a^m \div a^n = a^{m - n}\)
  • \((a^m)^n = a^{mn}\)
  • \(a^0 = 1\)