Chapter 7.2, Problem 3CYU

To determine

To Simplify: The Given expression

  $\frac{m^6{r}^5{p}^3}{m^5{r}^2{p}^3}$

Answer to Problem 3CYU

The simplified expression is $m{r}^3$ .

Explanation of Solution

Given information:

  $\frac{m^6{r}^5{p}^3}{m^5{r}^2{p}^3}$

Concept Used:

Quotient of powers: It states that to divide two powers with same base, subtract the exponent.

For example, let a be any non-zero number and m and n be any integer.

  $\frac{a^m}{a^n}=a^{m-n}$

Zero Exponent Property:Any non-zero number raised to the power zero is 1.

Example:let a be any non-zero number

  $a^0=1$

Calculation:

  $\frac{m^6{r}^5{p}^3}{m^5{r}^2{p}^3}$

(Group the powers with the same base)

  $=\left(\frac{m^6}{m^5}\right)\left(\frac{r^5}{r^2}\right)\left(\frac{p^3}{p^3}\right)$

Using Quotient of Powers

  $=m^{6-5}{r}^{5-2}{p}^{3-3}$

Simplify.

  $=m^1{r}^3{p}^0$

Using Zero Exponent Property

  $\begin{array}{l}=m{r}^3\cdot 1\\ =m{r}^3\end{array}$