Once your learners are confidently working with positive and negative integer and fractional indices, they are ready to change the base in problems involving indices.

Section A asks pupils to fill in the missing indices in statements such as ⅟9 = 3ˀ, which involves changing the base. The section begins with integer indices and progresses to include negative, fractional and finally negative fractional indices.

In section B, there are 9 terms with varying bases that are to be rewritten in the form 2ⁿ. Here n is sometimes an algebraic expression such as 6q + 6.

Section C sees students solving equations based on indices and different bases. The first two questions are scaffolded to aid learners.

Pupils in need of a challenge? Section D requires them to solve two further equations simultaneously.