Brackets With Indices Worksheet

Brackets with indices at a glance

The laws of indices are rules for simplifying expressions involving powers (indices) with the same base. These expressions can be numeric or algebraic. This topic involves application of one of the laws of indices – dealing with single brackets and indices, distributing the power outside the bracket across the terms inside the bracket. 

When working with numerical expressions with a single number base, we follow the order of operations and apply the law for brackets with indices. We then evaluate to get the final answer. When working with expressions with an algebraic base, we use the law for brackets with indices; our goal here is to simplify the expression fully. The final answer will usually still contain algebraic terms.

Misconceptions often arise where students forget to apply the power to any coefficients within the bracket. We can extend to more challenging problems, including dealing with fractions and fractional indices. 

Students may be asked to apply algebra and geometry skills in the same question – for example, solving practice questions using area, volume and surface area to brackets with indices. They may also be required to work backwards from the final answer to find a missing power.

Before studying this topic, it is important that students are secure with basic algebraic manipulation of algebraic expressions, simplifying expressions, expanding brackets and factorising.

Looking forward, students can progress with more indices worksheets and to additional algebra worksheets for example a solving equations worksheet or simultaneous equations worksheet.

For more teaching and learning support on Algebra our GCSE maths lessons provide step by step support for all GCSE maths concepts.