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.

01

If two exponential terms having same base are in division form, the quotient of them is equal to the difference of the exponents of same base.

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

02

If two exponential terms having same exponent with different bases are in division form, the quotient of them is equal to the quotient of the bases raised to the power of the exponent.

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

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Evaluate $\displaystyle \large \lim_{x \to 0} \normalsize \dfrac{e^{x^2}-\cos{x}}{x^2}$

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