The laws of exponents are fundamental rules in mathematics that simplify calculations involving powers and indices. Whether multiplying, dividing, or raising numbers to a power, these fundamental laws of exponents are required for calculations with accuracy. In this guide, we break down each law of exponents with easy-to-understand examples.

What are the Laws of Exponents
Solved Examples on Laws of Exponents
Practice Questions on Laws of Exponents

What are the Laws of Exponents

Law	a and b are non-zero integers and m and n are any integers	ab and cd are rational numbers and m and n are any integers
1	a^m × aⁿ = a^m+n	(ab)^m × (ab)ⁿ = (ab)^m+n
2	a^maⁿ = a^m−n	(ab)^m ÷ (ab)ⁿ = (ab)^m−n
3	(a^m)ⁿ = (aⁿ)^m = a^mn	{(ab)^m}ⁿ = {(ab)ⁿ}^m = (ab)^mn
4	(ab)ⁿ = aⁿbⁿ	(ab · cd)ⁿ = (ab)ⁿ × (cd)ⁿ
5	(ab)ⁿ = aⁿbⁿ	( a/b c/d )ⁿ = (a/b)ⁿ (c/d)ⁿ
6	a⁰ = 1	(ab)⁰ = 1

Solved Examples on Laws of Exponents

Evaluate:

(i) 1⁰ + 2⁻³ + 3⁻³

(ii) (5⁻⁴ + 8⁻⁹)⁰ × 2⁻²

(iii) (7⁻⁹ ÷ 7⁻¹⁵) × 7⁻⁸

Solution:

(i) 1⁰ + 2⁻³ + 3⁻³ = 1 + 12³ + 13³ = 1 + 18 + 127 = 216 + 27 + 8216 = 251216

(ii) (5⁻⁴ + 8⁻⁹)⁰ × 2⁻² = 1 × 2⁻² = 12² = 14

(iii) (7⁻⁹ + 7⁻¹⁵) × 7⁻⁸ = 7⁻⁹7⁻¹⁵ × 7⁻⁸ = 7^{−9−(−15)} × 7⁻⁸ = 7⁶ × 7⁻⁸ = 7⁶⁻⁸ = 7⁻² = 17² = 149

Practice Questions on Laws of Exponents

Evaluate:

(i) (6⁻¹ + 12⁻¹) × 5⁻¹

(ii) (2⁻³ × 3⁻²) + 7⁻¹

Frequently Asked Questions on Laws of Exponents

1. How to handle different bases with the same power?

Expressions with different bases and same power can be simplified using the law $a%5En%20%C3%97b%5En%20%3D%20(ab)%5En$

2. What is the zero exponent rule?

The zero exponent rule states that any non-zero number raised to the power of 0 is equal to 1. Let a be a non-zero number. $a%5E0%20%3D%201$

3. What is the power of a power rule?

The power of the power rule states that when raising a power to another power, multiply the exponents. $(a%5Em)%5En%20%3D%20a%5E%7B(m%20%2B%20n)%7D$

4. What are the laws of exponents?

The laws of exponents are fundamental rules in mathematics that simplify calculations involving powers and indices

Admissions Open for 2026-27

CXVI Roman Numerals	10000 in Words	Area	104 in Roman Numerals
Series	63 in Roman Numerals	66 in Roman Numerals	94 in Roman Numerals
Table of 556	Circumference of A Circle	Table of 649	86 in Roman Numerals
Table of 196	Table of 54	Simple Interest Questions	Table of 621
Table of 378	Table of 18	Table of 323	Table of 997

Laws of Exponents: Rules, Formulas & Easy Examples

Table of Contents