Chapter 7, Problem 24SGR

To determine

To Simplify: The expression ${\left(\frac{6x{y}^{11}{z}^9}{48x^{6}y{z}^{-7}}\right)}^0$

Answer to Problem 24SGR

  ${\left(\frac{6x{y}^{11}{z}^9}{48x^{6}y{z}^{-7}}\right)}^0=1$

Explanation of Solution

Given information:

The expression ${\left(\frac{6x{y}^{11}{z}^9}{48x^{6}y{z}^{-7}}\right)}^0$

Concept and Formula Used:

Rule of exponent.

  $a^{-n}=\frac{1}{a^n},a^0=1,\frac{a^m}{a^n}=a^{m-n}$

Calculation:

The given expression is

  $\begin{array}{l}{\left(\frac{6x{y}^{11}{z}^9}{48x^{6}y{z}^{-7}}\right)}^0\\ \text{Using }\frac{a^m}{a^n}=a^{m-n}\\ {\left(\frac{6x{y}^{11}{z}^9}{48x^{6}y{z}^{-7}}\right)}^0={\left(\frac{1}{8}{x}^{1-6}{y}^{11-1}{z}^{9-\left(-7\right)}\right)}^0\\ {\left(\frac{6x{y}^{11}{z}^9}{48x^{6}y{z}^{-7}}\right)}^0={\left(\frac{1}{8}{x}^{-5}{y}^{10}{z}^{16}\right)}^0\\ \text{Using }{a}^0=1\\ {\left(\frac{6x{y}^{11}{z}^9}{48x^{6}y{z}^{-7}}\right)}^0=1\end{array}$

Conclusion:

  ${\left(\frac{6x{y}^{11}{z}^9}{48x^{6}y{z}^{-7}}\right)}^0=1$