Year 10 - Maths
The laws of indices - raising a power to a power
Arithmetic procedures: index laws
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit pupils learn how to manipulate indices and perform calculations without conversion by understanding index laws.
Lesson Summary
You will learn to use the laws of indices to simplify a power raised to another power.
Key Notes
- The index tells you how many identical terms you must multiply together.
- By studying the structure of multiplication, you can see how the index will change.
- When multiplying powers with the same bases, the indices can be summed.
- This process can be made quicker as repeated addition can be more efficiently calculated through multiplication.
- (a^b)^c = a^(bc)
Vocabulary To Learn
- Index: An exponent is a number positioned above and to the right of a base value. It indicates repeated multiplication. An alternative word for this is index (plural indices).
- Coefficient: A numerical coefficient is a constant multiplier of the variables in a term.
- Power: 16 is the fourth power of 2. Alternatively this can be written as 2^4 which is read as "2 to the power of 4".
Common Mistakes To Avoid
- Forgetting to raise the coefficient to the power as well as the power term.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The index tells you how many identical terms you must multiply together. By studying the structure of multiplication, you can see how the index will change.
2. Use this key word in a maths sentence and explain it clearly. 'Index'
An exponent is a number positioned above and to the right of a base value. It indicates repeated multiplication. An alternative word for this is index (plural indices). Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Forgetting to raise the coefficient to the power as well as the power term. Correction: Highlight that everything in the bracket is being affected by the power. By showing examples where the bracket is written in expanded form and then the repeated multiplication helps with this.
More Lessons In This Unit
- Advanced problem solving with the laws of indices Study Guide
- Checking and securing understanding of calculating with fractions and decimals Study Guide
- Checking and securing understanding of calculations involving negative numbers Study Guide
- Checking and securing understanding of converting between fractions and decimals Study Guide
- Checking and securing understanding of LCM and HCF Study Guide
- Checking and securing understanding of prime factorisation Study Guide
- Checking and securing understanding of roots and integer indices Study Guide
- Converting any recurring decimal to a fraction Study Guide
- Problem solving with the laws of indices Study Guide
- The laws of indices - division Study Guide
- The laws of indices - fractional exponents Study Guide
- The laws of indices - multiplication Study Guide
- The laws of indices - negative and zero exponents Study Guide
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