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Exponents with Negative Bases Worksheet | Algebra 1 & 8th Grade Math Practice

Exponents with Negative Bases Worksheet | Algebra 1 & 8th Grade Math Practice

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

8 July 2026

pdf, 69.58 KB
pdf, 69.58 KB

A worksheet on exponents (powers) with negative bases. All the expressions in the exercises contain an exponent with a negative base with or with out parenthesis. Solutions are included.

Simplify your indices topic planning with this comprehensive, no-prep Exponents and Powers with Negative Bases Worksheet! This printable practice resource features 28 carefully structured questions designed to master a critical algebraic concept: evaluating bases with mixed signs. It explicitly tests the vital difference between expressions wrapped in brackets and expressions without them. Perfect for secondary maths classrooms, this resource includes a complete worked solutions mark scheme to make marking completely effortless!

Whether you need a quick homework assignment, daily starters, cover work, independent practice, or a revision review for GCSE exam prep, this worksheet has you covered.

What is Included in This Resource?

  • Comprehensive 28-Problem Practice Sheets: High-utility maths exercises designed to build student calculation confidence and reinforce index laws and sign rules.
  • Scaffolded Concept Coverage:
    Evaluating Negative Bases inside Brackets: Master how even powers yield a positive output and odd powers yield a negative output (e.g. evaluating (-2) squared vs (-2) cubed)
    Evaluating Expressions without Brackets: Reinforce the crucial structural rule that a power attached to a base without brackets applies only to the number, meaning the negative sign stays out front (e.g. evaluating -2 to the power of 4).
    Powers of Ten and Constants: Practice rapid calculations with varying bases, including regular digits, one, and ten raised to various powers.
  • Complete Worked Solutions / Mark Scheme: A detailed key that shows the direct answer for every single exercise—perfect for student self-assessment or quick teacher marking!

Ways to Use This in Your Classroom:

  • Independent Practice / Homework: Assign it right after your index laws lesson to solidify negative base evaluation.
  • Maths Starters / Bell Ringers: Cut the worksheet into smaller sections to use as daily sign-rule drills across a full week of lessons.
  • No-Prep Cover Work: The clear layout and comprehensive mark scheme mean you can just print, copy, and leave it for a cover teacher at a moment’s notice.
  • GCSE Revision / Remediation: Use it to diagnose and patch up foundational arithmetic gaps before moving into complex algebraic manipulation topics. Curriculum & Exam Board Alignment:UK National Curriculum (Key Stage 3 & 4):KS3 Mathematics (Number): Use positive integer powers and associate powers of 10 with numbers in standard form; employ standard conventional notation for the priority of operations, including brackets and powers.GCSE Mathematics (Foundation & Higher Tier): Meets specifications for AQA, Edexcel, and OCR by reinforcing calculations with powers and directed numbers, particularly highlighting priority rules without a calculator.

Get this resource as part of a bundle and save up to 29%

A bundle is a package of resources grouped together to teach a particular topic, or a series of lessons, in one place.

Bundle

Exponents & Powers with Negative Bases Fractions Worksheets Bundle + Answers

Three worksheet on exponents (powers) with positive and negative bases. There is one worksheet on exponents with positive or negative integers as bases, one worksheet on exponents with negative integers as bases and one worksheet on exponents with positive or negative integers or fractions as bases. In the exercises, students have to evaluate exponents with positive or negative bases and evaluate expressions involving such exponents, brackets addition and/or subtraction. Solutions to all worksheets are included. **Master Indices and Powers with Positive, Negative, Integer, and Fractional Bases!** Give your students the ultimate practice pack to conquer indices and powers! Evaluating exponents with negative numbers, brackets, and fractions can be incredibly confusing for secondary school maths students. This comprehensive, no-prep bundle brings together three targeted resources explicitly designed to eliminate common misconceptions—like understanding the zero index law, working with negative fractions, and recognising the crucial difference between (-3) squared and -5 squared. Whether you need homework tasks, independent classwork, cover work, or quick assessments, this complete value pack has you covered. **What is Included in This Bundle?** * **Resource 1: Indices with Positive and Negative Bases (8 Pages)** – A fantastic introduction targeting basic positive/negative integer rules and distinguishing when the negative sign is inside vs. outside the brackets. * **Resource 2: Advanced Order of Operations (4 Pages)** – Multi-step expressions that challenge students to apply index rules within complex maths strings using BIDMAS/BODMAS. * **Resource 3: Indices with Integers and Fractions (6 Pages)** – Advanced practice covering whole numbers, zero indices, and positive/negative fractional bases raised to odd and even powers. * **Complete Answer Keys** – Full step-by-step solutions are included for every single problem to make marking a breeze or to allow for quick student self-checking! **Perfect For:** * Key Stage 3 (KS3) and Key Stage 4 (KS4) maths classrooms * Years 7, 8, 9, 10, and GCSE foundation/higher students * Homework tasks or independent classwork * Starter activities, warm-ups, or exit tickets * Extra practice and intervention for struggling learners **Aligned with the UK National Curriculum for Mathematics:** *** Key Stage 3 Number:** Use integer powers and associated roots (square, cube and higher), recognise powers of 2, 3, 4, 5 and distinguish between exact representations of roots and their decimal approximations. * **Key Stage 4 / GCSE Mathematics:** Calculate with roots, and with integer and fractional indices. Understand the structure of calculating with positive, negative, and fractional bases.

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