Chapter 2.1, Problem 8GP

Solution

To simplify the expression ${\left(\frac{x^4{y}^{-2}}{x^3{y}^6}\right)}^3$ and property used.

The value of ${\left(\frac{x^4{y}^{-2}}{x^3{y}^6}\right)}^3$ is $x^3{y}^{-24}$ and property used are power of quotient ${\left(\frac{a}{b}\right)}^m=\frac{a^m}{b^m}$ , $b\ne 0$ , power of power ${\left(a^n\right)}^m=a^{nm}$ and negative exponent $a^{-m}=\frac{1}{a^m},a\ne 0$ ..

Given:

Expression: ${\left(\frac{x^4{y}^{-2}}{x^3{y}^6}\right)}^3$ .

Concept Used:

Power of quotient ${\left(\frac{a}{b}\right)}^m=\frac{a^m}{b^m}$ , $b\ne 0$ , power of power ${\left(a^n\right)}^m=a^{nm}$ and negative exponent $a^{-m}=\frac{1}{a^m},a\ne 0$ ..

Calculation:

The power of quotient property is used to solve the question.

  $\begin{array}{c}{\left(\frac{x^4{y}^{-2}}{x^3{y}^6}\right)}^3=\frac{\left(x^{4x3}{y}^{-2x3}\right)}{\left(x^{3x3}{y}^{6x3}\right)}\\ =\frac{x^{12}{y}^{-6}}{x^9{y}^{18}}\\ =x^3{y}^{-24}\end{array}$

Thus, simplified expression is $x^3{y}^{-24}$ .