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Chapter 10: Exponents and Powers

    Introduction

    Powers with Negative Exponents

    Laws of Exponents

    Use of Exponents to Express Small Numbers in Standard Form

    Comparing very large and very small numbers

    Exercise 10.1

    Exercise 10.2

    What Have We Discussed?

    Enhanced Curriculum Support

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Chapter 10: Exponents and Powers > Introduction

Introduction

Imagine you can jump up and down on a trampoline. Every time you jump up, the jumping distance from the trampoline doubles. So, if you start at 1 foot tall, after one jump, you will be 2 feet tall. After two jumps, you will be feet tall, and so on.

Now, let's say you jump up and down five times. How tall would you be? Well, we can use exponents to find out. The exponent in this case is 5, and the base is 2. This means that we are multiplying 2 by itself 5 times. So, if you jump up and down on a trampoline five times, you will be feet tall!

2 × 2 × 2 × 2 × 2 = 32

Imagine you have a magic plant that grows twice as tall every day. If the plant starts at 1 inch tall, after one day, it will be 2 inches tall. After two days, it will be inches tall, and so on.

Now, let's say you leave the plant for five days. How tall would it be? Again, we can use exponents to find out. The exponent in this case is and the base is .

This means that we are multiplying 2 by itself 5 times.

25 = 2 × 2 × 2 × 2 × 2

So, if you leave your magic plant for five days, it will be inches tall!

We read 25 as 2 raised to the 5.

We know that:

2m = 2 × 2 × 2 × 2 × ... × 2 × 2 ... (m times)

Mass of earth is 5,970,000,000,000,000,000,000,000 kg. We have already learnt in earlier class how to write such large numbers more conveniently using exponents, as, 5.97 × kg.

Let us now find what is 2−2 is equal to?

2−2 = =