Chapter 7.2, Problem 32PPS

To determine

To Simplify: The Given expression

  $\frac{p^{12}{t}^7{r}^2}{p^2{t}^{7}r}$

Answer to Problem 32PPS

The simplified expression is $p^{10}r$ .

Explanation of Solution

Given information:

  $\frac{p^{12}{t}^7{r}^2}{p^2{t}^{7}r}$

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:

  $\frac{p^{12}{t}^7{r}^2}{p^2{t}^{7}r}$

(Group the powers with the same base)

  $=\left(\frac{p^{12}}{p^2}\right)\left(\frac{t^7}{t^7}\right)\left(\frac{r^2}{r}\right)$

Using Quotient of Powers

  $=p^{12-2}{t}^{7-7}{r}^{2-1}$

Simplify.

  $=p^{10}{t}^0{r}^1$

Using Zero Exponent Property

  $=p^{10}\cdot 1\cdot r^1$

  $=p^{10}r$