🔗 Negative and Fractional Indices

About Negative and Fractional Indices

A negative index does not make a number negative, and a fractional index is a root rather than a division — those two sentences resolve most of the confusion in this topic, and both are best learned by seeing the equivalent forms side by side rather than by memorising rules. This matching worksheet puts them there. The left column holds an index form; the right column holds its exact value, shuffled, and the pupil draws the line between them. Two minus signs are kept carefully apart throughout: a negative power appears on a positive base, so nobody has to disentangle a negative index from a negative number at the same time as learning what one means. Every fractional index is applied to a base that genuinely has that root — sixteen to the half is offered, fifteen to the half never is — so no answer is ever an approximation. Every value on the page is distinct, which the matching requires: two rows with the same target would leave both unanswerable. The levels move from negative powers, through reciprocals, to square roots, to cube roots, and finally to negative fractional indices where both ideas combine. Each level prints as a clean A4 sheet with its own separate answer key. Its on-screen twin is Negative Index Reciprocal Drag.

Common questions

Does a negative index make the answer negative?

No — it gives the reciprocal. Every base on this worksheet is positive so the two ideas stay apart.

Are the roots exact?

Yes. Fractional indices are only applied to bases that genuinely have that root, so no answer is an approximation.

Can two rows share an answer?

No. Every value on a page is distinct, which the matching requires.

How do the levels progress?

Negative powers, reciprocals, square roots, cube roots, then negative fractional indices.