Exponents
Exponents are the power of any number or variable.
Example:- 2⁻², 4⁶, a⁴, x⁷ & 5⁻³
Where,
2, 4, a, x & 5 are the base.
While -2, 6, 4, 7 & -3 are the exponents.
What are the Laws of Exponents?
Laws of exponents are used to solve the problems where integers have powers.
Different types of Laws of Exponents are:-
List of the Laws of Exponents-
a^m × a^n = a^m+n
a^m ÷ a^n = a^m-n
a^m × b^m = (ab)^m
a^m ÷ b^m = (a÷b)^m
(a^m)ⁿ = (a)^mn
1. Laws of exponents for multiplication
a^m × a^n = a^m+n
Here we have a formula of exponents for multiplication-
Where,
a is the base, m & n are the exponents.
It is used where the bases are the same.
How to use the law of exponents for multiplication, understand with the example:-
Evaluate 2⁻⁷ × 2⁸
Solve:-
= 2⁻⁷ × 2⁸
{We will use the law of exponents for multiplication for the same base}
= a^m × a^n = a^m+n
= 2⁻⁷ × 2⁸ = 2⁻⁷⁺⁸
= 2¹
Here we get our answer 2¹.
2. Laws of exponents for the division
a^m ÷ a^n = a^m-n
Here we have a formula of exponents for division-
Where,
a is the base, m & n are the exponents.
It is used where the base is the same.
How to use the law of exponents for division, understand with the example:-
Evaluate 4⁵ ÷ 4⁻¹
Solve:-
= 4⁵ ÷ 4⁻¹
{We will use the law of exponents for the division of the same base}
= a^m ÷ a^n = a^m-n
= 4⁵ ÷ 4⁻¹ = 4⁵⁻⁽⁻¹⁾
= 4⁵⁺¹
= 4⁶
Here we get our answer 4⁶.
3. Laws of exponents for different bases & same powers
a^m × b^m = (ab)^m
Here we have a formula of exponents for different bases & same powers-
Where,
a & b are the bases, m is the exponent.
It is used where the bases are different & it works in multiplication.
How to use the law of exponents for different bases, understand with the example:-
Evaluate 4⁵ × 5⁵
Solve:-
= 4⁵ × 4⁵
{We will use the law of exponents for multiplication of the same base}
= a^m × b^m = (ab)^m
= 4⁵ × 5⁵ = (4×5)⁵
= (4×5)⁵
= 20⁵
Here we get our answer 20⁵.
