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The chapter on "Indices" in mathematics deals with powers, exponents, and the rules for manipulating them. Here are some of the key concepts:


What are the laws of indices?
Laws of indices provide us with rules for simplifying calculations or expressions involving powers of the same base. This means that the larger number or letter must be the same.

For example,

25×23=28x10÷x4=x6
We cannot use laws of indices to evaluate calculations when the bases are different

For example,

25×33x10÷y4


What are the 6 laws of indices?
The 6 laws of indices are:

Multiplying indices
Dividing indicies
Brackets with indices
Power of 0
Negative indices
Fractional indices
For examples and practice questions on each of the rules of indices, as well as how to evaluate calculations with indices with different bases

Laws of indices table
Moving up the rows we get 2 times larger per row.

Moving down the rows we get 2 times smaller per row.


1. Basics of Indices (Exponents)

An index or exponent tells you how many times to multiply a number by itself. For example:


a^n = a \times a \times a \dots \text{(n times)}

*Exponent* or **Index**: The power to which the base is raised (e.g., n in a^n).

2. Laws of Indices

These rules help simplify expressions with indices:

Product Law:

Quotient Law:

Power of a Power:

Power of a Product:

Power of a Quotient:


3. Special Exponents

Zero Power: (where )

Negative Exponents:

Fractional Exponents:

For example, , and .



4. Simplifying Expressions with Indices

Use the laws of indices to simplify expressions with multiple terms and operations.

Example:


\frac{(x^3 \times y^2)}{x \times y^3} = x^{3-1} \times y^{2-3} = x^2 \times y^{-1} = \frac{x^2}{y}

5. Scientific Notation

Indices are used in scientific notation to represent very large or very small numbers.

Example: represents 3,500,000.


Let me know if you'd like examples or practice problems on any specific part!