Chapter 7.2, Problem 37PPS

To determine

To Simplify: The Given expression

  $\frac{k^4{m}^3{p}^2}{k^2{m}^2}$

Answer to Problem 37PPS

The simplified expression is $k^{2}m{p}^2$ .

Explanation of Solution

Given information:

  $\frac{k^4{m}^3{p}^2}{k^2{m}^2}$

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.

  $\frac{a^m}{a^n}=a^{m-n}$

Calculation:

  $\frac{k^4{m}^3{p}^2}{k^2{m}^2}$

(Group the powers with the same base)

  $=\left(\frac{k^4}{k^2}\right)\left(\frac{m^3}{m^2}\right)p^2$

Using Quotient of Powers

  $=k^{4-2}{m}^{3-2}{p}^2$

Simplify

  $=k^2{m}^1{p}^2$

  $=k^{2}m{p}^2$