Prior Content: Basic Operations +-x/
Possible Next Steps: Simplifying Basic Expressions, Differentiation, Properties of Numbers, Standard Form
Contents
- 1.1 Basic Laws of Indices
- 1.2 The Power Law Expanded (ab)n
- 2.1 Power of 0
- 3.1 Negative Powers
- 3.2 Fractional Powers (1 as numerator)
- 3.3 Fractional Powers numerator not 1, possibly negative
- 4.1 Rewriting Bases
- Whole Topic Summary Resources (Including Past Paper Questions)
1.1 Basic Laws of Indices
Teaching Videos, Exercises & Activities
Tutorial Videos
Corbett Maths Laws of Indices
Online Platforms (with Videos & Exercises)
Activities & Resources
- Dr Austin Maths
- Investigating Algebraic Powers Activity (Editable Word | PDF | Answers)
- Maths 4 Everyone
- Pixi Maths
- Multiplication, Division & Power Law ppt
- Division Law Tarsia & Solution
- Andy Lutwyche (TES, free login to download)
- Indices Codebreakers
- Defuse The Bomb – Indices
- Clumsy Clive on Indices
- Simplifying Indices Match Up
- Indices Spiders
- Indices (Algebraic) Codebreaker
- Indices Match Up
- Pyramid Puzzles – Simplifying Indices 1
- Building Blocks – Indices
- Indices Matching
- Algebraic Indices Codbreaker
- Indices – Fill In The Blanks
Worksheets
- Dr Austin Maths
- Laws of Indices Practice Strips (Editable Word | PDF | Answers)
- Laws of Indices Odd One Out (Editable Word | PDF | Answers)
- Laws of Indices Match-Up (Editable Word | PDF | Answers)
- Simplifying Using Power Laws Practice Strips (Editable Word | PDF | Answers)
- Simplifying Using Power Laws Match-Up (Editable Word | PDF | Answers)
- Corbettmaths
- Laws of Indices Practice Questions & Solutions
- Laws of Indices Worksheet & Solutions
- Laws of Indices AQA Level 2 Practice Questions (Q1-5) & Solutions
- Daniel Burke Indices Decode the Joke PDF or ppt
- Dr Austin Maths
- Algebraic Laws of Indices Practice Grid (Editable Word | PDF | Answers)
- Simplifying Using Laws of Indices Practice Strips (Editable Word | PDF | Answers)
- Maths 4 Everyone
- Pixi Maths
- Teachit.co.uk Worksheet
Dr Frost Resources
Dr Frost Video
K432: Laws of Indices for Multiplying Powers.
K433: Laws of Indices for Dividing Powers.
K434: Laws of Indices for Raising a Power to a Power.
K435: Expand a Single Bracket Using Index Laws.
K149: Multiply Algebraic Terms With Powers.
K151: Divide Algebraic Terms With Powers.
Dr Frost Slides & Activities
- All in one summary sheet
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 158a: Use laws of indices for multiplying powers with numeric bases.
- 158b: Use laws of indices for dividing powers with numeric bases.
- 158c: Use laws of indices for raising a power to a power with a numeric base.
- 158d: Use laws of indices for both multiplying and dividing powers.
- 158e: Use laws of indices for multiplying, dividing and power of a power.
- 158g: Determine the unknown power in an expression involving index laws.
- 158h: Determine the base in an expression involving index laws with positive indices, given its numeric equivalent.
- 194a: Use laws of indices for multiplying powers with algebraic bases.
- 194b: Use laws of indices for terms with numerical bases and algebraic powers.
- 194c: Use laws of indices for dividing powers with algebraic bases.
- 194d: Multiply algebraic terms with powers.
- 194e: Divide algebraic terms with powers.
- 194g: Use laws of indices for raising a power to a power with an algebraic base.
- 194h: Simplify an expression using multiple index laws with a single algebraic variable.
- 194l: Simplify an expression using multiple index laws with multiple algebraic variables.
- 194m: Split a fraction using index laws.
- 194n: Determine the unknown power in an expression involving index laws with positive indices given its algebraic equivalent.
- 252e: Expand a single bracket with each term involving one variable or constant, using index laws.
- 252f: Expand a single bracket with each term involving multiple variables or constants, using index laws.
- 158: Exam Practice: Numerical index laws (basic)
- 194: Exam Practice: Algebraic index laws (basic)
- 252: Exam Practice: Expanding a single bracket
Extension Materials
1.2 The Power Law Expanded (ab)n
Teaching Videos, Exercises & Activities
Tutorial Videos
Online Platforms (with Videos & Exercises)
Activities & Resources
- Andy Lutwyche (TES, free login to download)
Worksheets
- Dr Austin Maths
- Simplifying Expressions Involving Brackets and Powers (Editable Word | PDF | Answers)
- Simplifying Harder Algebraic Indices Practice Strips (Editable Word | PDF | Answers)
- Corbettmaths
- Laws of Indices Worksheet (Q6) & Solutions
- Laws of Indices AQA Level 2 Practice Questions (Q6-11) & Solutions
- Maths 4 Everyone
Dr Frost Resources
Dr Frost Video
K439: Raise an Algebraic Term to a Positive Integer Power.
Dr Frost Slides & Activities
- Dr Frost Slides (4)
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
Extension Materials
Videos & Other Multimedia
2.1 Power of 0
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
Online Platforms (with Videos & Exercises)
Activities & Resources
- Pixi Maths
Worksheets
- Dr Austin Maths
- Power of Zero Practice Strips (Editable Word | PDF | Answers)
Dr Frost resources
Dr Frost Video
Dr Frost Slides & Activities
- All in one summary sheet
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 158f: Raise a number to the power of 0.
- 194f: Raise an algebraic term to the power of 0.
- 158: Exam Practice: Numerical index laws (basic)
- 194: Exam Practice: Algebraic index laws (basic)
Further Practice
- Practise Questions
EXTENSION MATERIALS
3.1 Negative Powers
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
Corbett Maths Negative Indices (Including Some Fractional)
Online Platforms (with Videos & Exercises)
Activities
- Pixi Maths
Worksheets
- Dr Austin Maths
- Negative Indices Practice Strips (Editable Word | PDF | Answers)
- Negative Indices Decode the Joke (Editable Word | PDF | Answers)
- Corbettmaths
Dr Frost resources
Dr Frost Video
K436: Raise a Number to a Negative Power.
K437: Raise a Fraction to a Negative Power.
K440: Raise an Algebraic Term to a Negative Power.
Dr Frost Slides & Activities
- Slides & Worksheet
Exam Practice
- Standard Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 298a: Raise a whole number to a negative integer power.
- 298b: Raise a fraction to a negative integer power.
- 298c: Raise a decimal to a negative integer power.
- 298d: Raise an algebraic term to a negative integer power.
- 298e: Write a fraction with an algebraic term on the denominator as a power of x
- 298f: Raise an algebraic fraction to a negative integer power.
- 298g: Determine the unknown power in an expression involving negative indices, given its equivalent value as a fraction.
- 298h: Determine the unknown base in an expression involving negative indices, given its equivalent as a fraction.
- 298i: Determine the unknown power or base in an expression involving negative indices, given its equivalent as a decimal.
- 298j: Determine the unknown power in an expression involving index laws and negative indices, given its numeric equivalent.
- 298k: Determine the unknown base in an expression involving index laws and negative indices, given its numeric equivalent.
- 298: Exam Practice: Negative indices
Further Practice
- Practise Questions
EXTENSION MATERIALS
3.2 Fractional Powers (1 as numerator)
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
Corbett Maths Fractional Indices (Up to 2:41)
Online Platforms (with Videos & Exercises)
Activities
- Pixi Maths
- Andy Lutwyche (TES, free login to download)
Worksheets
- Dr Austin Maths
- Fractional Indices Practice Strips (Editable Word | PDF | Answers)
- Fractional Indices Match-Up (Editable Word | PDF | Answers)
- Fractional and Negative Indices True or False (Editable Word | PDF | Answers)
- Corbettmaths
Dr Frost resources
Dr Frost Video
K689: Raise a Number to a Fractional Power. (Up to 1:25)
K691: Raise a Fraction to a Fractional Power. (Up to 0:34)
Dr Frost Slides & Activities
- Slides & Worksheet
Exam Practice
- Standard Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 394a: Raise a number to the power of one half.
- 394b: Raise a number to the power of a unit fraction.
- 394c: Determine the unknown power in an expression involving unit fractions as indices, given its numeric equivalent.
- 394d: Raise a fraction to the power of a unit fraction.
- 394j: Raise an algebraic term to the power of a positive unit fraction.
- 394n: Write a power with a unit fractional index as a surd expression.
- 394: Exam Practice: Fractional indices
Further Practice
- Practise Questions
EXTENSION MATERIALS
3.3 Fractional Powers numerator not 1, possibly negative
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
Corbett Maths Fractional Indices (From 2:41)
Online Platforms (with Videos & Exercises)
Activities
- Pixi Maths
Worksheets
- Dr Austin Maths
- Harder Indices Practice Strips (Editable Word | PDF | Answers)
- Harder Indices Odd One Out (Editable Word | PDF | Answers)
- Harder Indices Crack the Code (Editable Word | PDF | Answers)
- Harder Indices Match-Up (Editable Word | PDF | Answers)
- Fractional and Negative Indices Christmas Colouring (Editable Word | PDF | Answers)
- Algebraic Indices Practice Strips (Editable Word | PDF | Answers)
- Corbettmaths
- Negative & Fractional Indices Practice Questions & Solutions
- Negative Indices Worksheet (Q9-10) & Solutions
- Fractional Indices Worksheet (Q3 Onwards) & Solutions
- Negative & Fractional Indices AQA Level 2 Practice Questions & Solutions
- Maths 4 Everyone
- Pixi Maths
- WW PPQ Compilations
Dr Frost resources
Dr Frost Video
K689: Raise a Number to a Fractional Power.
K691: Raise a Fraction to a Fractional Power.
K693: Raise an Algebraic Term to a Fractional Power.
K690: Raise a Number to a Fractional and Negative Power.
K692: Raise a Fraction to a Fractional and Negative Power.
K694: Raise an Algebraic Term to a Fractional and Negative Power.
K438: Determine an Unknown Power e.g. 2y=1/8.
Dr Frost Slides & Activities
- Slides & Worksheet
Exam Practice
- Standard Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 394e: Raise a number to the power of a non-unit fraction.
- 394f: Raise a fraction to the power of a non-unit fraction.
- 394g: Determine the unknown power in an expression involving non-unit fractions as indices, given its numeric equivalent.
- 394h: Raise a number to the power of a negative fraction.
- 394i: Raise a fraction to the power of a negative fraction.
- 394k: Raise an algebraic term to the power of any positive fraction.
- 394l: Raise an algebraic term to the power of a negative fraction.
- 394m: Raise an algebraic fraction to the power of a negative fraction.
- 394o: Write a power with a non-unit fractional index as a surd expression.
- 394p: Write a surd expression in one variable as a power of that variable (or value).
- 394q: Write a collection of terms in the form axb
- 394r: Simplify an algebraic fraction using index laws with negative and fractional powers and surd notation.
- 394s: Write a fraction as a collection of terms by splitting the fraction.
- 394t: Raise an algebraic expression in standard form to a fractional power and convert back to standard form.
- 194i: Simplify an expression using multiple index laws with a single algebraic variable and fractional indices.
- 194k: Raise an algebraic term containing fractional indices to a positive integer power.
- 395a: Solve equations given in the form x-1 = a
- 395b: Solve equations given in the form x-a = b
- 395c: Solve equations given in the form x1/a = b
- 395d: Solve equations given in the form xa/b = c resulting in integer solutions.
- 395e: Solve equations given in the form xa/b = c resulting in solutions in surd form.
- 395f: Solve equations given in the form x-a/b = c
- 395g: Solve equations requiring rearrangement, leading to xa=b where a is a fraction.
- 395h: Solve equations where a root or fractional power is involved requiring operations with surds.
- 395i: Solve equations with negative and fractional indices, then manipulate these values.
- 194: Exam Practice: Algebraic index laws (basic)
- 394: Exam Practice: Fractional indices
- 395: Exam Practice: Solving equations involving negative and fractional powers and surds
Further Practice
- Practise Questions
EXTENSION MATERIALS
4.1 Rewriting Bases
TEACHING VIDEOS, EXERCISES & ACTIVITIES
Tutorial Videos
Corbett Maths Equations with Indices (From 6:19)
Maths By Fives Exponential Equations Examples
Online Platforms (with Videos & Exercises)
Activities
- Andy Lutwyche (TES, free login to download)
Worksheets
- Access Maths
- Dr Austin Maths
- Change of Base Practice Strips (Editable Word | PDF | Answers)
- Solving Equations with Unknown Indices Practice Strips (Editable Word | PDF | Answers)
- Corbettmaths
- Laws of Indices AQA Level 2 Practice Questions (Q11 Onwards) & Solutions
- Just Good Maths “Simplify to powers of 3 or 5, then apply laws of indices” Worksheet (TES Account Required)
- Maths 4 Everyone
- mathshelper.co.uk Equating Powers Worksheet
- WW PPQs Compilation Rewriting Bases Word Doc or PDF
Dr Frost resources
Dr Frost Video
Whole Topic Video
K767: Use Change of Base to Form a Linear Formula.
K438: Determine an Unknown Power e.g. 2y=1/8.
Dr Frost Slides & Activities
- Slides (42-45)
- Worksheet (Word) or PDF
Exam Practice
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 358a: Express a power using a different base.
- 358b: Use change of base to form a linear formula.
- 358c: Use index laws and change of base to write as a single index.
- 358d: Solve equations by transforming to the same base, leading to a linear equation.
- 358e: Change the subject of a formula by transforming to the same base.
- 485d: Solve an equation where indices can be equated, leading to a quadratic equation.
- 485e: Solve a quadratic equation in terms of an exponential term of the form ax (no logarithms).
- 358: Exam Practice: Expressing a power using a different base
- 485: Exam Practice: Solving hidden quadratic equations (no logs or trigonometric functions)
Further Practice
EXTENSION MATERIALS
Whole Topic Summary Resources (Including Past Paper Questions)
Download Indices PPQs as WW Powerpoint for Edexcel IGCSE, AQA GCSE, Edexcel GCSE or OCR GCSE (or all GCSE together)
Other Whole Topic Resources
Worksheets
- Dr Austin Maths
- Powers and Roots Revision Practice Grid (Editable Word | PDF | Answers)
- Corbettmaths
- Equations Involving Indices/Roots AQA Level 2 Practice Questions & Solutions
- Maths 4 Everyone