EDGE Math 8

Example 2

Simplify each expression. Assume that is a nonzero real number.

a. $\frac{a^{5}}{a^{3}}$

b. $\frac{a^{3}}{a^{5}}$

Solution

Use the definition of a positive integer exponent.

a. $\frac{a^{5}}{a^{3}} = \frac{a \cdot a \cdot a \cdot a \cdot a}{a \cdot a \cdot a}$

If you will cancel out the common factors, you will get $a \cdot a = a^{2} .$

Thus, $\frac{a^{5}}{a^{3}} = a^{2} .$

b. $\frac{a^{3}}{a^{5}} = \frac{a \cdot a \cdot a}{a \cdot a \cdot a \cdot a \cdot a}$

If you will cancel out the common factors, you will get $\frac{1}{a \cdot a} = \frac{1}{a^{2}} .$

Thus, $\frac{a^{3}}{a^{5}} = \frac{1}{a^{2}} .$