Year 10 - Maths
The laws of indices - multiplication
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 multiply two powers where the bases are the same.
Key Notes
- When multiplying two terms, you can sometimes write this more simply.
- If the powers have the same base, then the powers can be combined into a single power.
- The exponent or index of the new power reflects this combination.
- By studying the structure of multiplication, you can see how the index will change.
- a^b × a^c = a^(b+c)
Vocabulary To Learn
- 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".
- 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.
- Commutative: An operation is commutative if the values it is operating on can be written in either order without changing the calculation.
- Associative: An operation is associative if a repeated application of the operation produces the same result regardless of how pairs of values are grouped.
Common Mistakes To Avoid
- When multiplying terms with coefficients, pupils also add the coefficients as well as the exponents.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
When multiplying two terms, you can sometimes write this more simply. If the powers have the same base, then the powers can be combined into a single power.
2. Use this key word in a maths sentence and explain it clearly. '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". Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: When multiplying terms with coefficients, pupils also add the coefficients as well as the exponents. Correction: Pupils should be encouraged to rewrite their expression using the associative and commutative laws, with the number parts grouped and powers grouped. This hopefully avoids this error as they can see it is the product of the numbers.
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 - negative and zero exponents Study Guide
- The laws of indices - raising a power to a power Study Guide
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