Chapter 7.2, Problem 2BGP

To determine

To Simplify: The Given expression

  ${\left(\frac{5x^{5}y}{6}\right)}^2$

Answer to Problem 2BGP

The simplified expression is $\frac{25x^{10}{y}^2}{36}$ .

Explanation of Solution

Given information:

  ${\left(\frac{5x^{5}y}{6}\right)}^2$

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:

  ${\left(\frac{5x^{5}y}{6}\right)}^2$

Using Power of Quotient

  $=\frac{5^2{\left(x^5\right)}^2{y}^2}{6^2}$

Simplify

  $=\frac{25x^{10}{y}^2}{36}$