Chapter 7.2, Problem 67PFA

To determine

To Find: The value of ‘m’ if expression ${\left(\frac{x^2{y}^3}{y^{2}z}\right)}^m=1$

Answer to Problem 67PFA

  $m=0$ option ‘C’ is correct.

Explanation of Solution

Given information:

The expression ${\left(\frac{x^2{y}^3}{y^{2}z}\right)}^m=1$

Concept and Formula Used:

Rule of exponent.

  $a^{-n}=\frac{1}{a^n},a^0=1,{\left(a\right)}^m={\left(a\right)}^n\text{ then }m=n$

Calculation:

The given expression is

  $\begin{array}{l}{\left(\frac{x^2{y}^3}{y^{2}z}\right)}^m=1\\ \text{Using }{a}^0=1\\ {\left(\frac{x^2{y}^3}{y^{2}z}\right)}^m={\left(\frac{x^2{y}^3}{y^{2}z}\right)}^0\\ \text{If }{\left(a\right)}^m={\left(a\right)}^n\text{ then }m=n\\ \text{Therefore }m=0\end{array}$

Conclusion:

  $m=0$ option ‘C’ is correct.