Chapter 7.2, Problem 24PPS

To determine

To Simplify: The Given expression

${\left(\frac{3t^6{u}^2{v}^5}{9tu{v}^{21}}\right)}^0$

Answer to Problem 24PPS

The simplified expression is $1$ .

Explanation of Solution

Given information:

${\left(\frac{3t^6{u}^2{v}^5}{9tu{v}^{21}}\right)}^0$

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:

  ${\left(\frac{3t^6{u}^2{v}^5}{9tu{v}^{21}}\right)}^0$

Using Zero Exponent Property

  $=\frac{3^0{\left(t^6\right)}^0{\left(u^2\right)}^0{\left(v^5\right)}^0}{9^0{t}^0{u}^0{\left(v^{21}\right)}^0}$

Simplify

  $=\frac{1\cdot t^0\cdot u^0\cdot v^0}{1\cdot 1\cdot 1\cdot v^0}$

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

  $=1$