Lesson Notes By Weeks and Term v4 - JHS 2

Lesson Video

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Performance objectives

• Identify the different laws of indices.
• Explain why each law is important.
• Apply the laws to solve problems.
• Simplify expressions using these laws.

Lesson summary

In our daily lives, we often deal with very large or very small numbers. For example, the population of Ghana is over 30 million, the distance to the sun is about 150 billion metres, and the size of a tiny bacterium is a very small fraction of a metre. Writing these numbers with all their zeros can be tiring and can lead to mistakes. Indices (or powers) give us a simple and powerful shorthand way to write and work with such numbers. This lesson will introduce the fundamental rules, or "laws," that govern how we work with indices, making complex calculations much easier.

Lesson notes

Part 1: What are Indices? (Review)

Before we learn the laws, let's remember what an index is. An index is a way of writing repeated multiplication.

Consider the expression 3⁴. The 3 is called the base. This is the number that is being multiplied. The 4 is called the index, exponent, or power. It tells us how many times to multiply the base by itself.

So, 3⁴ means 3 × 3 × 3 × 3. When we calculate this, we get 3 × 3 = 9, then 9 × 3 = 27, and finally 27 × 3 = 81. Therefore, 3⁴ = 81.