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Laws of indices formula

The laws of indices formula as it is used in GCSE Mathematics, taken from the GCSE Mathematics formula sheet.

The formula

am×an=am+n,am÷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}

How to use it in the exam

  • Write the formula down before substituting — most mark schemes award a method mark for a correct, clearly quoted formula.
  • Check every quantity is in consistent units before you substitute, then substitute in one step so the working stays easy to follow.
  • Show the rearrangement rather than jumping to the answer, and give the final value to the accuracy the question asks for.

Related algebra & number formulas

Quadratic formula
x=−b±b2−4ac2ax = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}
Difference of two squares
a2−b2=(a+b)(a−b)a^2 - b^2 = (a + b)(a - b)
Negative & fractional indices
a−n=1an,a1n=ana^{-n} = \dfrac{1}{a^n}, \quad a^{\frac{1}{n}} = \sqrt[n]{a}
Compound interest
A=P(1+r100)nA = P\left(1 + \dfrac{r}{100}\right)^n

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