Imagine a single maize grain. After planting, one plant produces about 800 grains. If all those grains are planted, each producing 800 more, how many grains after three cycles? This multiplication (800 x 800 x 800) is inconvenient to write. Mathematicians developed a shorthand called index notation.
▸ Index Notation — When a number is multiplied by itself repeatedly, we write it compactly using an index (also called an exponent or power). The general form is a^n, where 'a' is the base and 'n' is the index.
Example: In 2^3, the base is 2 and the index is 3. This means 2 x 2 x 2.
Let's look at how we read index notation:
◆ Diagram: Table showing Expression, Read As, and Value:
2^3: '2 to the power of 3' or '2 cubed' = 8
5^2: '5 squared' = 25
10^4: '10 to the power of 4' = 10,000
3^5: '3 to the power of 5' = 243
7^1: '7 to the power of 1' = 7
Note: Any number raised to the power 1 equals itself: a^1 = a.
★ Real-world — Bacteria Growth:
A colony doubles every hour. Start: 50 bacteria. After t hours, the number of bacteria is 50 x 2^t. After 6 hours, there are 50 x 2^6 = 50 x 64 = 3,200 bacteria.
Audio narration — reads aloud, works offline
In your own words, summarise the main idea of this lesson.