Year 10 - Maths
The laws of indices - negative and zero exponents
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 with negative and zero exponents.
Key Notes
- A calculator can be helpful to explore what happens when the exponent is zero or negative.
- Any term with an exponent of zero is equal to one.
- A negative exponent tells you how many times you need to multiply the reciprocal of the base.
- Negative exponents appear when writing very small numbers in standard form.
Vocabulary To Learn
- Reciprocal: A reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1
- Indices: 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).
Common Mistakes To Avoid
- Any number with an index of 0 equates to 0
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A calculator can be helpful to explore what happens when the exponent is zero or negative. Any term with an exponent of zero is equal to one.
2. Use this key word in a maths sentence and explain it clearly. 'Reciprocal'
A reciprocal is the multiplicative inverse of any non-zero number. Any non-zero number multiplied by its reciprocal is equal to 1. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Any number with an index of 0 equates to 0. Correction: Reiterate the division of any number by itself is 1. This applies with laws of indices too. E.g 8^4 / 8^4 = 8^0. Any number divided by itself gives 1, therefore 8^0 = 1. For more advanced understanding, algebraic can be used instead of 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 - multiplication Study Guide
- The laws of indices - raising a power to a power Study Guide
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