Laws of Indices
Index laws are rules for working with powers (indices). These rules apply to all bases and are essential for simplifying algebraic expressions and working in scientific notation.
What You Need to Know
Key Concept Diagram
Multiplication: a^m x a^n = a^(m+n) - add the indices
Division: a^m / a^n = a^(m-n) - subtract the indices
Power of a power: (a^m)^n = a^(mn) - multiply the indices
Zero index: a^0 = 1 for any non-zero base; negative index: a^(-n) = 1/a^n
Key Vocabulary
Index (Exponent)
The power to which a base is raised; the small raised number
Base
The number being multiplied by itself in a power expression
Scientific notation
A way to write very large or small numbers using powers of 10
Reciprocal
1 divided by a number; a^(-1) is the reciprocal of a
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Simplify: x^3 x x^5
Question 2
Simplify: y^6 / y^2
Question 3
What is the value of 5^0?
Key Concepts Summary
- ●Multiplication: a^m x a^n = a^(m+n) - add the indices
- ●Division: a^m / a^n = a^(m-n) - subtract the indices
- ●Power of a power: (a^m)^n = a^(mn) - multiply the indices
- ●Zero index: a^0 = 1 for any non-zero base; negative index: a^(-n) = 1/a^n