Bab 1 Matematik tingkatan 3 (kssm): 1.2B Hukum Indeks- Pembahagian dan Dikuasakan

Introduction

This tutorial will guide you through the process of dividing and raising numbers using index notation, as presented in the video by Cikgu Chong. Understanding these concepts is essential for mastering mathematical operations involving indices, which are commonly used in various fields such as science and engineering.

Step 1: Understanding Index Notation

Index notation is a way to express numbers using exponents. The general form is:

• a^n, where:
  • a is the base
  • n is the exponent (or index)

Key Points

• The exponent indicates how many times the base is multiplied by itself.
• For example, 3^2 means 3 multiplied by itself, which equals 9.

Step 2: Division of Numbers in Index Notation

When dividing numbers that are expressed in index notation, you can subtract the exponents of the same base.

Formula

If a^m and a^n are two terms with the same base a, the division is expressed as:

• a^m / a^n = a^(m-n)

Example

• For 5^3 / 5^1:
  • Subtract the exponents: 3 - 1 = 2
  • Thus, 5^3 / 5^1 = 5^2 = 25

Practical Advice

• Always ensure that the bases are the same before dividing.
• Simplifying the exponents helps in calculating the division efficiently.

Step 3: Raising a Number to an Index

To raise a number to a power, simply multiply the number by itself according to the exponent.

Formula

If a is the base and n is the exponent, the operation is expressed as:

• (a^m)^n = a^(m*n)

Example

• For (2^3)^2:
  • Multiply the exponents: 3 * 2 = 6
  • Thus, (2^3)^2 = 2^6 = 64

Practical Advice

• This rule is particularly useful in simplifying complex expressions.
• Always check to ensure that you correctly multiply the exponents.

Step 4: Combining Division and Raising

You may encounter problems that involve both division and raising to an index.

Example

• For (3^4 / 3^2)^3:
  • First, divide: 3^4 / 3^2 = 3^(4-2) = 3^2
  • Then raise to the power: (3^2)^3 = 3^(2*3) = 3^6 = 729

Common Pitfalls

• Watch out for mistakes in exponent subtraction or multiplication.
• Ensure all bases are consistent when applying these rules.

Conclusion

Understanding how to divide and raise numbers in index notation is crucial for solving mathematical problems efficiently. By mastering these steps, you will be better prepared for more complex mathematical concepts. Practice with various examples to reinforce your skills, and don't hesitate to revisit this tutorial whenever needed. Happy learning!