There are two types of quotient rules of exponents in mathematics and here is the list of division laws of indices in algebraic form to use them as formulas in solving the problems.

The quotient of exponents with same base is equal to the difference of the powers with the same base.

$\dfrac{b^{\displaystyle m}}{b^{\displaystyle n}}$ $\,=\,$ $b^{\displaystyle \,m-n}$

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

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

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