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Edexcel International AS Maths: Pure 1

Revision Notes

Home / International AS / Maths: Pure 1 / Edexcel / Revision Notes / 1. Algebra & Functions / 1.1 Laws of Indices & Surds / 1.1.1 Laws of Indices


1.1.1 Laws of Indices


What do I need to know about laws of indices?

  • Laws of indices (or index laws – 'index' is the singular, 'indices' is the plural) allow you to simplify and manipulate expressions involving powers
  • The index laws you need to know and use are summarised here:List of index laws, A Level & AS Level Pure Maths Revision Notes

 

Changing the base of a term

  • Sometimes you can use index laws to change the base of a term, and thereby simplify an expression involving terms with apparently different bases
  • For example begin mathsize 20px style 9 to the power of 4 equals left parenthesis 3 squared right parenthesis to the power of 4 equals 3 to the power of 2 cross times 4 end exponent equals 3 to the power of 8 end style
  • Using the above can then help with problems like begin mathsize 20px style 9 to the power of 4 divided by 3 to the power of 7 equals 3 to the power of 8 divided by 3 to the power of 7 equals 3 to the power of 8 minus 7 end exponent equals 3 to the power of 1 equals space 3 end style

Exam Tip

  • Index laws only work with terms that have the same base, so something like 23 × 52 cannot be simplified using index laws. 

Worked Example

Index laws example, A Level & AS Level Pure Maths Revision Notes



  • 1. Algebra & Functions
    • 1.1 Laws of Indices & Surds
      • 1.1.1 Laws of Indices
        • 1.1.2 Manipulating Surds
          • 1.1.3 Surds - Rationalising the Denominator
          • 1.2 Quadratics
            • 1.2.1 Quadratic Graphs
              • 1.2.2 Discriminants
                • 1.2.3 Completing the square
                  • 1.2.4 Solving Quadratic Equations
                    • 1.2.5 Further Solving Quadratic Equations (Hidden Quadratics)
                    • 1.3 Simultaneous Equations
                      • 1.3.1 Linear Simultaneous Equations - Elimination
                        • 1.3.2 Linear Simultaneous Equations - Substitution
                          • 1.3.3 Quadratic Simultaneous Equations
                          • 1.4 Inequalities
                            • 1.4.1 Linear Inequalities
                              • 1.4.2 Quadratic Inequalities
                                • 1.4.3 Inequalities on Graphs
                                • 1.5 Polynomials
                                  • 1.5.1 Expanding Brackets
                                    • 1.5.2 Factorising Expressions
                                    • 1.6 Graphs of Functions
                                      • 1.6.1 Sketching Polynomials
                                        • 1.6.2 Reciprocal Graphs - Sketching
                                          • 1.6.3 Solving Equations Graphically
                                            • 1.6.4 Proportional Relationships
                                              • 1.6.5 Modelling with Functions
                                              • 1.7 Transformations of Functions
                                                • 1.7.1 Translations
                                                  • 1.7.2 Stretches
                                                    • 1.7.3 Reflections
                                                  • 2. Coordinate Geometry
                                                    • 2.1 Equation of a Straight Line
                                                      • 2.1.1 Basic Coordinate Geometry
                                                        • 2.1.2 Parallel & Perpendicular Gradients
                                                          • 2.1.3 Equation of a Straight Line
                                                            • 2.1.4 Modelling with Straight Lines
                                                          • 3. Trigonometry
                                                            • 3.1 Basic Trigonometry
                                                              • 3.1.1 Trigonometry - Definitions
                                                                • 3.1.2 Right-Angled Triangles
                                                                  • 3.1.3 Non-Right-Angled Triangles
                                                                  • 3.2 Radian Measure
                                                                    • 3.2.1 Radian Measure
                                                                      • 3.2.2 Trigonometry Exact Values
                                                                      • 3.3 Trigonometric Functions
                                                                        • 3.3.1 Graphs of Trigonometric Functions
                                                                          • 3.3.2 Transformations of Trigonometric Functions
                                                                        • 4. Differentiation
                                                                          • 4.1 Differentiation
                                                                            • 4.1.1 Definition of Gradient
                                                                              • 4.1.2 Definition of Derivatives
                                                                                • 4.1.3 Differentiating Powers of x
                                                                                  • 4.1.4 Gradients, Tangents & Normals
                                                                                    • 4.1.5 Second Order Derivatives
                                                                                  • 5. Integration
                                                                                    • 5.1 Integration
                                                                                      • 5.1.1 Fundamental Theorem of Calculus
                                                                                        • 5.1.2 Integrating Powers of x


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                                                                                      Author: Roger

                                                                                      Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.


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