Chapter 7.2, Problem 35PPS

To determine

To Simplify: The Given expression

$-\frac{2f^3{g}^2{h}^0}{8f^2{g}^2}$

Answer to Problem 35PPS

The simplified expression is $-\frac{f}{4}$ .

Explanation of Solution

Given information:

$-\frac{2f^3{g}^2{h}^0}{8f^2{g}^2}$

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:

  $-\frac{2f^3{g}^2{h}^0}{8f^2{g}^2}$

(Group the powers with the same base)

  $=-\frac{2}{8}\left(\frac{f^3}{f^2}\right)\left(\frac{g^2}{g^2}\right)h^0$

Using Quotient of Powers

  $=-\frac{2}{8}\left(f^{3-2}\right)\left(g^{2-2}\right)h^0$

Simplify.

  $=-\frac{1}{4}\cdot f^1\cdot g^0\cdot h^0$

Using Zero Property

  $=-\frac{1\cdot f\cdot 1\cdot 1}{4}$

Simplify

  $=-\frac{f}{4}$