Laws of Exponents at Algebra Den

Arithmetic

Additive Identity
Arithmetic Progression
Associative Property
Averages
Brackets
Closure Property
Commutative Property
Conversion of Measurement Units
Cube Root
Decimal
Distributivity of Multiplication over Addition
Divisibility Principles
Equality
Exponents
Factors
Fractions
Fundamental Operations
H.C.F / G.C.D
Integers
L.C.M
Multiples
Multiplicative Identity
Multiplicative Inverse
Numbers
Percentages
Profit and Loss
Ratio and Proportion
Simple Interest
Square Root
Unitary Method

Algebra

Cartesian System
Order Relation
Polynomials
Probability
Standard Identities & their applications
Transpose

Geometry

Basic Geometrical Terms
Circle
Curves
Angles
Define Line, Line Segment and Rays
Non-Collinear Points
Parallelogram
Rectangle
Rhombus
Square
Three dimensional object
Trapezium
Triangle
Quadrilateral

Trigonometry

Trigonometry Ratios

Data-Handling

Arithmetic Mean
Frequency Distribution Table
Graphs
Median
Mode
Range

Videos
Solved Problems

Home >> Exponents >> Laws of Exponents >>

Laws of Exponents

a^m X aⁿ = a^m+n a^m ÷ aⁿ = a^m-n ( a^m )ⁿ = a^{m n} a^m X b^m = (ab)^m a^m ÷ b^m = (a/b)^m
a⁰ = 1 a^-m

Laws of Exponents are of following types

Multiplication of Same Base with Different Exponents (a^m X aⁿ = a^m+n )

Division of Same Base with Different Exponents (a^m aⁿ = a^m-n)

One Base with Exponent of Exponent[(a^m )ⁿ = a^{m n} ]

Multiplication of different Bases with Same Exponent a^m X b^m = (ab)^m

Division of different Bases with Same Exponent a^m ÷ b^m = (a/b)^m

Base with Zero Exponent is always equal to 1 (a⁰ = 1)

Base with negative exponents i.e. a^-m = 1/m

All these Laws are explained with examples in the above respective links.