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

Using indices, we can show a number times itself many times or as another way of writing a square or cube root. Indices make complex calculations that involve powers easier.

Part ofMathsNumber

Letters or numbers to the power of zero

Explore the refreshed revision guide 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 \(j^2 \div j^2 = j^0\) (dividing rule) and \(j^2 \div j^2 = 1\), which means \(j^0 = 1\).

Laws of indices - summary

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

Negative indices

Raising a power to a power

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