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This topic extends the laws of indices to negative powers (reciprocals) and fractional powers (roots), so expressions like 8^(2/3) and x⁻² can be evaluated and simplified. It's examined right across GCSE and iGCSE Maths. Learn it free on eClassroom through guided worked examples and instantly-marked exam-style questions.
How you do it
A negative index means the reciprocal, so x to the minus 2 is 1 over x squared. A fractional index means a root: the denominator gives the root and the numerator gives the power. Take the root first — the numbers stay smaller.
Before you start
You need index laws and roots before this makes sense. Assessed at Higher tier. From here the path runs to algebraic manipulation at A-Level.
What you learn
Indices don’t stop at whole numbers. Negative powers mean reciprocals and fractional powers mean roots — two ideas that unlock a whole class of Higher questions. x 1/2 × x 1/2 = x 1/2 + 1/2 = x — which fits, since √x × √x = x. The course works through negative indices, fractional indices and combining the rules. Every section has instant-feedback practice questions matched to Edexcel iGCSE 4MA1 and the other major GCSE boards, and the course finishes with full exam-style questions you mark yourself.
Related Topics
Fractional & Negative Indices is part of the Number strand of our free GCSE maths courses, studied in Higher tier. There are 3 teaching sections and 2 fully worked examples, plus 3 sets of check questions. It sits alongside Fractions & Exact Calculation, Indices, Order of Operations and Ordering & Place Value in the same strand. Endless extra practice on this strand is available on the Number revision engine, which generates a fresh question each time.
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