Indices

Summary and Exam Tips for Indices

Indices is a subtopic of Numbers, which falls under the subject Mathematics in the IB MYP curriculum.

Exponents, also known as Powers or Indices, indicate how many times a number is used in multiplication. There are four fundamental rules for operations with powers:

1. Multiplication: When multiplying indices with equal bases, add the powers: $a^m \times a^n = a^{m+n}$.
2. Division: When dividing indices with equal bases, subtract the powers: $\frac{a^m}{a^n} = a^{m-n}$.
3. Power of a Power: Multiply the powers: $(a^m)^n = a^{m \times n}$.
4. Negative Power: Convert a negative power to positive by taking the reciprocal: $a^{-n} = \frac{1}{a^n}$.

It is crucial that the base of the indices is equal to apply these rules.

The Absolute Value of a number represents its distance from zero, disregarding any negative sign. For example, the absolute value of $-6$ is 6, denoted as $|-6| = 6$. The absolute value operation can also be expressed as $\text{abs}()$. It is important to remember that the absolute value of a subtraction remains the same regardless of the order: $|a-b| = |b-a|$.

Exam Tips

• Understand the Basics: Ensure you are comfortable with the basic rules of indices, such as multiplication, division, and power of a power. Practice problems to reinforce these concepts.

• Equal Bases: Always check that the bases are equal before applying any of the indices rules. This is a common mistake that can lead to incorrect answers.

• Negative Powers: Remember that negative powers can be converted into positive by taking the reciprocal. This is a handy trick to simplify expressions.

• Absolute Value: Practice problems involving absolute values, especially those that involve subtraction, to understand how the order of numbers does not affect the result.

• Practice, Practice, Practice: The best way to master indices is through consistent practice. Use a variety of problems to test your understanding and improve your skills.