Chapter 7.2, Problem 23PPS

To determine

To Simplify: The Given expression

${\left(\frac{3x{y}^4}{5z^2}\right)}^2$

Answer to Problem 23PPS

The simplified expression is $\frac{9x^2{y}^8}{25z^4}$ .

Explanation of Solution

Given information:

${\left(\frac{3x{y}^4}{5z^2}\right)}^2$

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.

  ${\left(\frac{a}{b}\right)}^m=\frac{a^m}{b^m}$

Calculation:

  ${\left(\frac{3x{y}^4}{5z^2}\right)}^2$

Using Power of Quotient

  $=\frac{3^2\cdot x^2{\left(y^4\right)}^2}{5^2{\left(z^2\right)}^2}$

Simplify

  $=\frac{9x^2{y}^8}{25z^4}$