MathematicsGCSE & IGCSEAlgebra & Number

Negative & fractional indices formula

The negative & fractional indices formula as it is used in GCSE Mathematics, taken from the GCSE Mathematics formula sheet.

The formula

a^{-n} = \dfrac{1}{a^n}, \quad a^{\frac{1}{n}} = \sqrt[n]{a}

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.

x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}

a^2 - b^2 = (a + b)(a - b)

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

A = P\left(1 + \dfrac{r}{100}\right)^n

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