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Laws of Exponents & Rules of Indices Practice Worksheet | Algebra Radicals

Laws of Exponents & Rules of Indices Practice Worksheet | Algebra Radicals

Subject: Mathematics

Age range: 14-16

Resource type: Worksheet/Activity

Last updated

25 September 2026

pdf, 99.71 KB
pdf, 99.71 KB

Master applying the laws of exponents and rules of indices with this 24-problem practice worksheet featuring complete step-by-step worked solutions!

Master the rules of indices and laws of exponents with this comprehensive, step-by-step practice worksheet resource! Designed to help students build mastery in algebraic simplification, this package guides learners through essential exponent properties using single-variable and multi-variable expressions.

Students will practice applying key rules including the product rule, quotient rule, power of a power rule, negative exponents, and multi-variable operations.

Features 24 carefully scaffolded problems that progressively increase in complexity, moving from basic power operations to multi-step expressions requiring order of operations with exponents.

Complete step-by-step worked solutions are provided for all 24 questions to make marking fast and facilitate independent student self-assessment.

Ideal for Key Stage 3, Key Stage 4, GCSE Maths, High School Algebra, classwork, homework, revision, or exam preparation.

Get this resource as part of a bundle and save up to 41%

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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GCSE IGCSE Number Worksheets Bundle - Fractions Percentages Indices Bounds +

A collection of 20 worksheets on various number topics from the GCSE/IGCSE syllabus. The following topics are included: * Rounding * Bounds * Calculator use * Percentages, fractions and decimals * Increasing or decreasing an amount by a percentage * Percentage of a quantity * The rules of indices * Factors, Multiples and Primes * Square and cube roots * Mixed operations between fractions, mixed numbers and whole numbers * HCF and LCM using prime factorisation * Recurring decimals * Simple interest * Compound interest * Operations With Positive and Negative Numbers * Order of operations * Standard form * Multiplying and dividing by powers of 10 * Adding and subtracting positive and negative numbers * Multiplying and dividing positive and negative numbers Detailed solutions are provided for each worksheet. Master core GCSE and IGCSE mathematics with this comprehensive, no-prep 20-worksheet Number resource pack! Packed with exam-style questions, complete step-by-step worked solutions, and a wide variety of topics, this collection is perfect for KS3 and KS4 revision, homework, and cover lessons. Covers fractions, percentages, index laws, upper/lower bounds, rounding, and calculator operations. ________________________________________ Looking for rigorous, no-prep math resources to help your students master essential Number topics? This highly comprehensive 20-worksheet pack is designed to fully align with UK GCSE and IGCSE math specifications. Whether you need structured cover lessons, targeted homework tasks, daily classroom practice, or an all-in-one exam revision booklet, this resource has you covered! Every single worksheet comes paired with complete step-by-step worked solutions, making grading an absolute breeze and allowing students to self-assess or peer-mark effectively. ________________________________________ **What Topics Are Covered?** 1. **Percentages & Conversions** • Converting seamlessly between fractions, decimals, and percentages. • Calculating the exact percentage of a given quantity. • Increasing and decreasing an amount by a percentage. 2. **Fractions & Core Arithmetic Operations** • Simplifying and writing fractions in their simplest form. • Converting fractions to exact percentages and decimals. 3. **The Rules of Indices (Laws of Indices)** • Multiplying and dividing terms using basic, fraction, and negative index laws. • Simplifying complex algebraic terms with brackets and single variables. • Working with dual-variable expressions involving negative bases. 4. **Upper & Lower Bounds (Error Intervals)** • Calculating upper and lower bounds for multi-step formulas. • Applying rounding bounds to fractional and multi-variable equations. • Solving limits for equations containing radicals and square roots. 5. **Foundational Number Skills** • Rounding integers to the nearest 10, 100, or 1000. • Rounding decimals to the nearest whole number or specific decimal places. • Listing factors, multiples, prime numbers, and prime factors. • Multi-step calculator practice using complex fractional expressions, fractions, and roots. ________________________________________ **Why Teachers Choose This Resource Pack:** • Zero Prep Needed: Just download, print, and you are ready to go! • Step-by-Step Solutions: Complete answer keys show exactly how to solve each problem, not just the final numerical answer. • Scaffolded Layout: Moves smoothly from basic numeric concepts up to advanced higher tier error bounds. • Universal, Clean Design: Styled neatly without distracting clutter, maximizing student focus during revision. ________________________________________ **Curriculum Alignment:** • Key Stage 4 (KS4): Perfect for Year 10 and Year 11 preparing for Higher and Foundation tiers. • Key Stage 3 (KS3): Great for Year 8 and Year 9 higher-tier extension or foundational work. • Exam Boards: Fully supports objectives for Edexcel, AQA, OCR GCSE, and Cambridge CIE / Oxford AQA IGCSE.

£18.90
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Laws of Exponents Bundle | Negative & Fractional Powers Practice Sheets

Premium 3-worksheet bundle on the rules of indices. Covers fractional index laws, radical form simplifications, and algebraic fractions with full worked keys! Develop your students' foundational algebraic confidence and index law fluency with this premium Rules of Indices Worksheet Bundle! Perfectly curated for Key Stage 3 extension blocks, GCSE Higher Tier revision, or A-Level transition preparation, this multi-resource bundle scaffolds skills flawlessly. **Core Worksheet Packs Included Inside:** • **Resource Pack 1 (Product & Quotient Laws):** Enforces the multiplication and division laws across integer bases and multi-variable monomials (including implicit powers of 1. • **Resource Pack 2 (Algebraic Fractions):** 8 rigorous simplifying grids featuring fractional coefficient reduction, negative indices, and multi-variable cuts (such as 21a^2b / 14ab^2 or -9xy^2 / 12xy). • **Resource Pack 3 (Fractional & Negative Indices):** 32 rigorous grids exploring rational powers, root conversions, and deep multi-variable expression reductions (such as 27a^6b^9 to the power of 2/3). • **Comprehensive Step-by-Step Solutions:** Fully worked answer keys accompany each worksheet pack to allow for immediate student self-marking, peer assessment, or quick cover work preparation. **Curriculum Alignment:** • Apply multiplication, division, power, and rational rules of indices to simplify nested terms • Reduce complex algebraic fractions using negative and fractional indices laws • Interconvert values between root radical structures and fractional exponents • Key Stage 3 Mathematics Mastery & GCSE Higher/Foundation preparation

£3.50
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Algebra & Functions Worksheets Bundle Factoring, Radicals, Indices

Algebra and functions 8-worksheet bundle covering simplifying expressions, index laws, factoring, surds, and bracket expansion with full step-by-step answer keys. Master essential algebra and functions concepts with this comprehensive 8-worksheet bundle designed for secondary math students. This printable resource collection covers foundational to advanced topics, offering rigorous practice with detailed step-by-step solutions for every problem. **Worksheets Included in This Bundle:** - Simplifying Expressions by Collecting Like Terms - Laws and Rules of Indices / Exponents - Advanced Rational Exponents & Fractional Index Laws - Factoring Linear Expressions & Monomial GCF - Factoring Quadratic Expressions & Difference of Squares - Simplifying Radicals & Surd Operations - Rationalising the Denominator with Surds & Conjugates - Expanding Single Brackets & Double Bracket Expressions **Key Features:** - 8 comprehensive printable student practice worksheets - Complete step-by-step answer key for quick marking, self-assessment, and guided learning - Clean, professional layout ready for immediate classroom use, homework, or exam prep

£6.30

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