Chapter 6.1, Problem 3E

To determine

Toexplain: The significance of Quotient of Powers Property.

Explanation of Solution

The quotient of powers property is used in two exponential expression when the base of the expression is same.

Consider two exponential expression that has same base $x^a,x^b$ .

The numbers $x^a,x^b$ can be multiply by adding the powers of both the expressions.

The quotient of power property can be mathematically expressed as:

  $x^a\cdot x^b=x^{a+b}$

Now take an example $2^3\cdot 2^5$ and use the quotient of powers property to explain how to use it.

  $\begin{array}{c}{2}^3\cdot 2^5=2^{3+5}\\ =2^8\end{array}$

It can be seen that the problem is much easier to solve with thequotient of powers property.