Chapter 7.2, Problem 4CYU

To determine

To Simplify: The Given expression

  $\frac{b^4{c}^6{f}^8}{b^4{c}^3{f}^5}$

Answer to Problem 4CYU

The simplified expression is $c^3{f}^3$ .

Explanation of Solution

Given information:

  $\frac{b^4{c}^6{f}^8}{b^4{c}^3{f}^5}$

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:

  $\frac{b^4{c}^6{f}^8}{b^4{c}^3{f}^5}$

(Group the powers with the same base)

  $=\left(\frac{b^4}{b^4}\right)\left(\frac{c^6}{c^3}\right)\left(\frac{f^8}{f^5}\right)$

Using Quotient of Powers

  $=b^{4-4}{c}^{6-3}{f}^{8-5}$

Simplify.

  $=b^0{c}^3{f}^3$

Using Zero Exponent Property

  $\begin{array}{l}=1\cdot c^3{f}^3\\ =c^3{f}^3\end{array}$