# Product Rules of Exponents

A mathematical identity that expresses a rule for multiplying the exponents to obtain their product is called the product rule of exponents.

In mathematics, there are two product laws and used as formulas to find the product of two or more multiplying exponents. Here is the list of product rules for exponents with proofs and examples for beginners.

### Product Rule of Exponents with same Base

The product of exponents with same base is equal to the sum of their powers with same base.

$b^{\displaystyle m} \times b^{\displaystyle n} \,=\, b^{\displaystyle \,m+n}$

### Power of a Product Rule

The product of same exponents with different bases is equal to the power of a product of their bases.

$b^{\displaystyle m} \times c^{\displaystyle m} \,=\, (b \times c)^{\displaystyle m}$

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