# Chapter 5 Polynomials and Polynomial Functions - 5.1 Use Properties of Exponents - 5.1 Exercises - Skill Practice - Page 334: 48

$\dfrac{a^m}{a^n}=a^{m-n}$

#### Work Step by Step

Since, $\dfrac{a^m}{a^n}=a^m \times \dfrac{1}{a^n}$ Also, $a^{-n}=\dfrac{1}{a^n}$ Thus, $a^m \dfrac{1}{a^n}=a^m a^{-n}$ ...(1) Now, we need to use the product of powers property. $a^{m}a^{-n}=a^{m-n}$ Equation (1) becomes: $a^m \dfrac{1}{a^n}=a^m a^{-n}=a^{m-n}$ This gives: $\dfrac{a^m}{a^n}=a^{m-n}$ Hence, the result has been verified.

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