Chapter 7.2, Problem 22PPS

To determine

To Simplify: The Given expression

  $\frac{c^4{d}^4{f}^3}{c^2{d}^4{f}^3}$

Answer to Problem 22PPS

The simplified expression is $c^2$ .

Explanation of Solution

Given information:

  $\frac{c^4{d}^4{f}^3}{c^2{d}^4{f}^3}$

Concept Used:

Quotient of powers: It states that to divide two powers with same base, subtract the exponent.

For example, let a be any non-zero number and m and n be any integer.

  $\frac{a^m}{a^n}=a^{m-n}$

Zero Exponent Property:Any non-zero number raised to the power zero is 1.

Example:let a be any non-zero number

  $a^0=1$

Calculation:

  $\frac{c^4{d}^4{f}^3}{c^2{d}^4{f}^3}$

(Group the powers with the same base)

  $=\left(\frac{c^4}{c^2}\right)\left(\frac{d^4}{d^4}\right)\left(\frac{f^3}{f^3}\right)$

Using Quotient of Powers

  $=c^{4-2}{d}^{4-4}{f}^{3-3}$

Simplify.

  $=c^2{d}^0{f}^0$

Using Zero Exponent Property

  $\begin{array}{l}=c^2\cdot 1\cdot 1\\ =c^2\end{array}$