Chapter 7.2, Problem 2CGP

To determine

To Simplify: The Given expression

  ${\left(\frac{2y^2}{3z^3}\right)}^2$

Answer to Problem 2CGP

The simplified expression is $\frac{4y^4}{9z^6}$ .

Explanation of Solution

Given information:

  ${\left(\frac{2y^2}{3z^3}\right)}^2$

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.

  $\frac{a^m}{b^m}=\frac{a^m}{b^m}$

Calculation:

  ${\left(\frac{2y^2}{3z^3}\right)}^2$

Using Power of Quotient

  $=\frac{2^2{\left(y^2\right)}^2}{3^2{\left(z^3\right)}^2}$

Simplify

  $=\frac{4y^4}{9z^6}$