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Index notation-Negative and fractional indices worksheet (with solutions)

Index notation-Negative and fractional indices worksheet (with solutions)

Subject: Mathematics

Age range: 11-14

Resource type: Worksheet/Activity

Last updated

25 October 2026

pdf, 115.53 KB
pdf, 115.53 KB

A worksheet on negative and fractional indices. Detailed solutions are included.

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

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Exponents / Laws of Indices Worksheets Bundle | Algebra Math Review Pack

Seven worksheets on simplifying expressions with indices. A practice on laws of indices, negative and fractional indices. Detailed solutions are included. Master exponential rules with this comprehensive, no-prep Exponents / Laws of Indices Worksheets Bundle | Algebra Math Review Pack! Aligned to Key Stage 3, Key Stage 4, and GCSE Higher Tier objectives, this extensive, ready-to-print resource packet covers the product rule, quotient rule, power of a power rule, and negative or fractional indices. Complete with highly detailed, step-by-step worked solutions, it is the ultimate time-saving tool for main lessons, homework packets, cover work, or exam revision. ________________________________________ Are your secondary mathematics students struggling with base numbers, fractional powers, or radical expressions? Simplify your maths lesson planning with this high-utility Laws of Exponents and Indices Resource Pack. This bundle contains 7 carefully structured student worksheets designed to build computational confidence and algebraic fluency across critical index concepts. Every single student problem page comes paired with a highly detailed, full-solution worked answer key that maps out the exact addition, subtraction, division, or root rules required to simplify each expression. It is perfect for student self-assessment, small group interventions, homework packets, cover lessons, or fast and easy teacher marking! **What's Inside this Worksheet Pack?** • **Core Laws of Indices (4 Student Pages):** Comprehensive practice introducing and reinforcing the product rule, quotient rule, power of a power rule, and zero index rules using both numeric bases and algebraic variables. • **Negative & Fractional Indices (2 Student Pages):** Rigorous practice questions tracking fractional conversions, reciprocal adjustments for negative powers, and evaluating numerical radical root values without a calculator. • **Solving Exponential Equations (1 Student Page):** Advanced problem sets requiring students to find a missing variable index by equating bases across complex rational terms and roots. • **Teacher Answer Keys (11 Pages):** Complete, step-by-step visual worked solutions matching every student layout page exactly. Why Teachers Love This Pack: • **Zero Prep Required:** Just print out the PDF pages and you are ready to go! • **Scaffolded Progressions:** Skills move logically from basic index operations to complex multi-step fractional transformations. • **Clean Layouts:** Generous workspace for students to neatly write down their expanded bases and power adjustments. • **Detailed Worked Keys:** Perfect for leaving with cover teachers or distributing digitally via a virtual learning environment (VLE) for independent revision. **Curriculum Alignment:** • **UK National Curriculum (GCSE Maths Higher Tier):** Objective N6 (Use index laws for multiplication, division, and powers of a power, including negative and fractional indices) and Objective A17 (Solve exponential equations by equating bases). • **International Frameworks:** Excellent for Year 9, Year 10, and Year 11 mathematics classes, as well as Higher Level IGCSE or foundational A-Level algebra bridging.

£8.80
Bundle

Math Worksheets Bundle - Order of Operations Integers Fractions Surds Radicals

A bundle of 10 worksheets (with detailed solutions) on Number topics appropriate for GCSE students. Each worksheet contains questions for students of various abilities. The topics covered by these worksheets include: * BIDMAS * Adding Integers * Subtracting Integers * Multiplying Integers * Dividing Integers * Mixed Operations Between Fractions, Mixed Numbers and Whole Numbers * Surds * Rules of Indices: Multiplication and Division * Fractional Indices * Negative and Fractional Indices The pack is ideal for use in revision sessions or for individual study. The solutions provided are very clear and explanatory. Master core arithmetic and number skills with this comprehensive, no-prep math worksheets resource pack! Perfect for KS3 and KS4 lessons, homework, and GCSE test prep, this resource features targeted practice for the order of operations (BIDMAS), integer operations, fraction arithmetic, and simplifying surds. Includes full, step-by-step worked solutions for effortless marking! ________________________________________ Looking for a rigorous, completely no-prep math resource to help your students build a flawless foundation in numbers and arithmetic? This comprehensive number resource pack is designed to perfectly align with UK GCSE/IGCSE math specifications and the National Curriculum. Whether you need structured cover lessons, targeted homework tasks, daily classroom practice, or an all-in-one exam revision booklet, this resource is ready to print and use immediately! Every single worksheet comes paired with a complete, fully worked step-by-step solution key. The answer keys explicitly demonstrate order of operations hierarchies, grouping rules, integer calculations, and surd expansion—making grading an absolute breeze and enabling effective student self-assessment or peer-marking. ________________________________________ **What Skills & Topics Are Covered?** 1. **Order of Operations (BIDMAS / BODMAS)** • Evaluating complex multi-step numerical expressions with brackets, indices, fractions, and multiplication. • Scaffolded problem solving ranging from foundational arithmetic up to complex bracket-within-bracket expressions. • Critical thinking worksheets where students must manually insert brackets to make mathematical equations true. 2. **Positive & Negative Integers** • Targeted worksheets focusing purely on adding integers with conflicting signs. • Structured sheets for subtracting positive and negative values from zero and dealing with double negatives. • Multiplying and dividing multi-digit integers, including fill-in-the-blank missing factor logic grids. 3. **Fractions Arithmetic & Mixed Operations** • Adding and subtracting proper fractions, improper fractions, and large mixed numbers with unlike denominators. • Multiplying and dividing complex fractional expressions, whole numbers, and multi-step mixed values. • Cross-simplifying equations to write complex final answers in their absolute simplest fractional form. 4. **Surds Mastery** • Simplifying square roots fully and converting radical integers into simpler coefficient form (writing in the form k root m). • Evaluating fraction surds and multiplying expressions with mismatched square roots. • Expanding and simplifying double brackets containing integers and surds using the FOIL/distribution method. ________________________________________ **Why Teachers Choose This Resource Pack:** • Zero Prep Needed: Save hours of planning—just download, print, and you are ready to go! • Step-by-Step Solutions: Complete answer keys explicitly show the order of calculation, making it incredibly clear for visual learners. • Scaffolded Practice: Each topic seamlessly transitions from basic conceptual checks to advanced, higher-tier exam-style applications. • Clean, Accessible Layout: Minimalist design avoids visual clutter, keeping student focus entirely on the calculations and formulas. ________________________________________ **Curriculum Alignment & Target Groups:** • Key Stage 3 (KS3): Perfect foundational and extension blocks for Year 7, Year 8, and Year 9. • Key Stage 4 (KS4): Ideal for Year 10 and Year 11 preparation across both Foundation and Higher GCSE/IGCSE tiers. • Exam Boards: Fully supports the curriculum objectives for AQA, Edexcel, OCR GCSE, and Cambridge CIE / Oxford AQA IGCSE exams. ________________________________________

£5.95
Bundle

Indices Laws Negative & Fractional Exponents Worksheets & Solutions

Master index laws, negative exponents, and fractional indices with this comprehensive bundle of practice worksheets and step-by-step worked solutions. Designed for middle and high school math students, this resource covers simplifying algebraic terms, applying exponent rules, converting between radicals and rational powers, and evaluating numerical expressions without a calculator. **What's Included:** - Scaffolded practice worksheets covering index laws, negative indices, and fractional exponents - Complete step-by-step worked solutions for every problem - Ready-to-print format for classroom practice, homework assignments, test prep, or substitute plans **Core Topics Covered:** - Applying multiplication and division index laws - Evaluating negative and fractional exponent expressions - Converting between radical form and fractional index form - Simplifying algebraic expressions with variables and exponents

£3.50
Bundle

Percentages, Indices & Factorisation Worksheets Bundle GCSE Algebra

Master percentages, indices, and algebraic factorisation with this comprehensive 8-worksheet bundle designed for GCSE and IGCSE math students! This extensive collection covers essential algebra and number topics, guiding students from foundational concepts to advanced problem-solving without calculators. **What is included:** * Converting between percentages, fractions, and decimals * Percentage increase, decrease, and reverse percentage problems * Index notation, negative indices, and fractional exponents * Multiplication and division index laws and exponential equations * Expanding single and double brackets * Factorising linear expressions and simple quadratics * Advanced quadratic factorisation and difference of two squares * Full step-by-step answer keys for every worksheet

£7.90
Bundle

Index Laws & Exponents Worksheets Negative Fractional Indices Practice Bundle

Master index notation and index laws with this comprehensive 3-worksheet bundle, covering negative exponents, fractional indices, and multiplication and division rules. Designed for middle and high school algebra students, these practice sheets guide learners from foundational concepts to advanced evaluations without calculators. **What is included:** * Negative and zero exponents practice * Fractional indices and radical conversions * Multiplication and division index laws * Full step-by-step answer keys for every problem

£3.40

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