Study Notes
Indices, also known as exponents or powers, indicate how many times a number is used in multiplication. The laws of indices include rules for multiplying, dividing, and raising powers, as well as converting negative powers to positive by taking the reciprocal.
- Exponent — the number that shows how many times to multiply the base. Example: In 2^3, 3 is the exponent, meaning 2 is multiplied by itself 3 times (2 × 2 × 2).
- Power — the result of raising a base to an exponent. Example: 3^2 is a power, which equals 9.
- Absolute Value — the distance of a number from zero, always positive. Example: The absolute value of -5 is 5, written as |-5| = 5.
Exam Tips
Key Definitions to Remember
- Exponent: The number that indicates how many times the base is multiplied by itself.
- Power: The result of raising a base to an exponent.
- Absolute Value: The non-negative value of a number without regard to its sign.
Common Confusions
- Confusing the base with the exponent.
- Forgetting to add exponents when multiplying powers with the same base.
- Misunderstanding that absolute value is always positive.
Typical Exam Questions
- What is 2^3? Answer: 8
- Simplify (3^2) × (3^3). Answer: 3^5 or 243
- What is the absolute value of -7? Answer: 7
What Examiners Usually Test
- Understanding and applying the laws of indices.
- Correctly calculating powers and absolute values.
- Simplifying expressions using indices rules.