Chapter 7.2, Problem 41PPS

To determine

To Simplify: The Given expression

$\frac{r^3{t}^{-1}{x}^{-5}}{t{x}^5}$

Answer to Problem 41PPS

The simplified expression is $\frac{r^3}{t^2{x}^{10}}$ .

Explanation of Solution

Given information:

  $\frac{r^3{t}^{-1}{x}^{-5}}{t{x}^5}$

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.

  $\frac{a^m}{a^n}=a^{m-n}$

Negative Exponent Property: $a^{-n}$ is the reciprocal of $a^n$ , where a is a non-zero number and n is an integer.

  $a^{-n}=\frac{1}{a^n}$

Calculation:

  $\frac{r^3{t}^{-1}{x}^{-5}}{t{x}^5}$

(Group the powers with the same base)

  $=\left(r^3\right)\left(\frac{t^{-1}}{t}\right)\left(\frac{x^{-5}}{x^5}\right)$

Using Quotient of Powers

  $=r^3{t}^{-1-1}{x}^{-5-5}$

Simplify

  $=r^3{t}^{-2}{x}^{-10}$

Using Negative Exponent Property

  $=r^3\frac{1}{t^2}\frac{1}{x^{10}}$

Simplify

  $=\frac{r^3}{t^2{x}^{10}}$