Brackets with Indices Worksheet

• Section 1 of the brackets with indices worksheet contains 48 skills-based brackets with indices questions, in 3 groups to support differentiation
• Section 2 contains 4 applied brackets with indices questions with a mix of worded problems and deeper problem solving questions
• Section 3 contains 4 foundation and higher level GCSE comprehensive exam practice questions on brackets with indices
• Answers and a mark scheme for all questions are provided
• Questions follow variation theory with plenty of opportunities for students to work independently at their own level
• All questions are created by fully qualified expert secondary maths teachers
• Suitable for GCSE maths revision for AQA, OCR and Edexcel exam boards
• Many additional algebra worksheets are available, including solving equations, the quadratic formula, and inequalities

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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.

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