# Exponent rules

The quantities are expressed in exponential notation in mathematics for some reasons. For doing some mathematical activities with exponential functions, the fundamental formulas of mathematics may not be useful. Hence, it requires some special properties and they are called the rules of exponents. Now, let’s learn the following three types of exponential properties with proofs to study the indices (or exponents) mathematically.

### Product Rules

There are two types of product laws in mathematics and they are used to multiply a quantity in exponential form by another quantity in exponential notation.

$(1).\,\,\,$ $b^m} \times b^n} \,=\, b^\,m+n$

$(2).\,\,\,$ $b^m} \times c^m} \,=\, (b \times c)^m$

### Quotient Rules

There are two types of division laws in mathematics, they are used to divide a quantity in exponential form by another quantity in exponential form.

$(1).\,\,\,$ $\dfrac{b^m}}{b^n}} \,=\, b^\, m-n$

$(2).\,\,\,$ $\dfrac{b^m}}{c^m}} \,=\, \bigg(\dfrac{b}{c}\bigg)^m$

### Power Rules

In mathematics, there are six types of power rules to find value of a quantity with exponent.

$(1).\,\,\,$ $\big(b^m}\big)^n} \,=\, b^\, m \times n$

$(2).\,\,\,$ $b^-m} \,=\, \dfrac{1}{b^m}$

$(3).\,\,\,$ $b^{\dfrac{1}{n}} \,=\, \sqrt[\displaystyle n]{b\,\,}$

$(4).\,\,\,$ $b^{\dfrac{m}{n}} \,=\, \sqrt[\displaystyle n]{b^m}$

$(5).\,\,\,$ $b^0 \,=\, 1$

$(6).\,\,\,$ $b^1 \,=\, b$

Latest Math Topics
Jun 26, 2023
Jun 23, 2023

Latest Math Problems
Jul 01, 2023
Jun 25, 2023
###### Math Questions

The math problems with solutions to learn how to solve a problem.

Learn solutions

Practice now

###### Math Videos

The math videos tutorials with visual graphics to learn every concept.

Watch now

###### Subscribe us

Get the latest math updates from the Math Doubts by subscribing us.