Chapter 6.1, Problem 3MRE

To determine

To calculate: The simplified form of the expression $\frac{15a^7{b}^8}{30a^2{b}^3}$.

Answer to Problem 3MRE

The simplified value of the expression $\frac{15a^7{b}^8}{30a^2{b}^3}$ is $\frac{a^5{b}^5}{2}$.

Explanation of Solution

Given information:

The expression $\frac{15a^7{b}^8}{30a^2{b}^3}$.

Formula used:

The simplest form of an algebraic fraction is when numerator and denominator have no common factor other than 1 and $-1$.

Law of division of powers $\frac{a^m}{a^n}=a^{m-n}$.

Calculation:

Consider the expression $\frac{15a^7{b}^8}{30a^2{b}^3}$.

Recall that the simplest form of an algebraic fraction is when numerator and denominator have no common factor other than 1 and $-1$ . Apply law of division of powers.

Strike out the common terms from numerator and denominator as,

  $\begin{array}{c}\frac{15a^7{b}^8}{30a^2{b}^3}=\frac{15a^{7-2}{b}^{8-3}}{15\cdot 2}\\ =\frac{a^5{b}^5}{2}\end{array}$

Thus, the simplified value of the expression $\frac{15a^7{b}^8}{30a^2{b}^3}$ is $\frac{a^5{b}^5}{2}$.