Year 10 - Maths
The laws of indices - fractional 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 fractional exponents.
Key Notes
- All of the index laws can be applied with fractional exponents.
- Using a calculator can help you to form an idea about how to evaluate a power containing a fractional exponent.
- You can reason that a power with a fractional exponent is equivalent to finding the square root of the base.
- √a = a^(1/2)
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.
Common Mistakes To Avoid
- Pupils multiply the base by the fractional exponent. e.g 25^(1/2) = 12.5
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
All of the index laws can be applied with fractional exponents. Using a calculator can help you to form an idea about how to evaluate a power containing a fractional exponent.
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: Pupils multiply the base by the fractional exponent. e.g 25^(1/2) = 12.5. Correction: The use of a calculator allows pupils to see the index of a fraction is not to be multiplied by the base. Embedding the laws of indices where two bases are the same and each number has an index of 1/2 helps recognize the 1/2 index as a square root.
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 - multiplication 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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