Chapter 7.2, Problem 31PPS

To determine

To Simplify: The Given expression

  ${\left(-\frac{5f^9{g}^4{h}^2}{f{g}^2{h}^3}\right)}^0$

Answer to Problem 31PPS

The simplified expression is $-1$ .

Explanation of Solution

Given information:

  ${\left(-\frac{5f^9{g}^4{h}^2}{f{g}^2{h}^3}\right)}^0$

Concept Used:

Power of a quotient: It states that in order to find the power of a quotient, find the power of the numerator and that of the denominator.

Example:let a and b be any non-zero number and m be any integer.

  ${\left(\frac{a}{b}\right)}^m=\frac{a^m}{b^m}$

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:

  ${\left(-\frac{5f^9{g}^4{h}^2}{f{g}^2{h}^3}\right)}^0$

Using Power of Quotient

  $=-\frac{5^0{\left(f^9\right)}^0{\left(g^4\right)}^0{\left(h^2\right)}^0}{f^0{\left(g^2\right)}^0{\left(h^3\right)}^0}$

Simplify

  $=-\frac{5^0\cdot f^0\cdot g^0\cdot h^0}{f^0\cdot g^0\cdot h^0}$

Using Zero Exponent Property

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

  $=-1$