There are two fundamental product laws for exponents in mathematics. One of them is used to multiply two or more exponents with the same base and other property is used to multiply two or more exponents with different bases mathematically for obtaining the product of them.
A product Rule for multiplying two or more exponents with the same base and its product is equal to the base raised to the power of sum of the exponents.
$b^{\displaystyle m} \times b^{\displaystyle n} \,=\, b^{\displaystyle \,m+n}$
A product rule for multiplying two or more exponents with different bases and the same exponents. The product of them is equal to the power of the product of the all the bases.
$b^{\displaystyle m} \times c^{\displaystyle m} \,=\, (b \times c)^{\displaystyle m}$
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