ML Aggarwal ICSE Class 9 Maths Ch-8 With Easy, Stepwise Solutions

MATHS CHAPTER – 8
Indices
Exercise – 8

Looks long and boring, right? What if we could write it in a short and smart way?
That’s exactly what indices help us do!.

In mathematics, indices (also called exponents or powers) offer a simple way to represent repeated multiplication of the same number.
For example:

Here, 2 is the base and 3 is the index or exponent. This tells us that 2 is multiplied by itself 3 times.

Indices help you simplify big numbers, solve algebraic expressions, and understand patterns in growth (like population or bacteria multiplying). They are also used in advanced math, science, computers, and engineering.

In short, indices are a small topic with a big impact. So get ready to explore the power of powers and make your calculations quicker and smarter!.

Indices are powerful tools in math, but even small mistakes can lead to big errors. Here are some helpful tips to keep your work clear and accurate:

1. Understand the Meaning of the Index

Don’t just see 2⁴ as a symbol — know that it means 2×2×2×2=16. Many students confuse it with 2×4=8, which is incorrect. The index tells how many times the base is multiplied by itself.

2. Never Multiply Base with Power

A common mistake is to do this:

The base and the exponent are not multiplied — the base is multiplied by itself as many times as the exponent says.

3. Apply Laws of Indices Only When Bases Are the Same

You can only add or subtract powers when the bases are the same.
Example :

So, never mix up different bases when applying laws.

4. Watch the Signs Carefully

Negative exponents or subtraction in powers can be tricky. Always double-check your signs.
Example:

5. Don’t Skip Writing Steps

Trying to do everything mentally increases chances of errors. Write down at least the key steps, especially when applying multiple laws in one problem.

6. Revise the Laws Regularly

Memorizing is not enough. Practice using the laws regularly so you don’t mix them up during tests.

Index Laws (Laws of Indices)

1. Product Law:

When the bases are the same, you can add the powers.
Example: