Chapter 7.2, Problem 28PPS

To determine

To Simplify: The Given expression

${\left(\frac{3n{p}^3}{7q^2}\right)}^2$

Answer to Problem 28PPS

The simplified expression is $\frac{9n^2{p}^6}{49q^4}$ .

Explanation of Solution

Given information:

${\left(\frac{3n{p}^3}{7q^2}\right)}^2$

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:

  ${\left(\frac{3n{p}^3}{7q^2}\right)}^2$

Using Power of Quotient

  $=\frac{3^2\cdot n^2{\left(p^3\right)}^2}{7^2{\left(q^2\right)}^2}$

Simplify

  $=\frac{9n^2{p}^6}{49q^4}$