Chapter 7.2, Problem 36PPS

To determine

To Simplify: The Given expression

  $\frac{12m^{-4}{p}^2}{-15m^3{p}^{-9}}$

Answer to Problem 36PPS

The simplified expression is $-\frac{4p^{11}}{5m}$ .

Explanation of Solution

Given information:

  $\frac{12m^{-4}{p}^2}{-15m^3{p}^{-9}}$

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:

  $\frac{12m^{-4}{p}^2}{-15m^3{p}^{-9}}$

(Group the powers with the same base)

  $=\left(\frac{12}{-15}\right)\left(\frac{m^{-4}}{m^3}\right)\left(\frac{p^2}{p^{-9}}\right)$

Using Quotient of Powers

  $=\left(\frac{12}{-15}\right)m^{-4-3}{p}^{2-\left(-9\right)}$

Simplify.

  $=\left(-\frac{4}{5}\right)m^{-1}{p}^{11}$

Using Negative Exponent Property

  $=\left(-\frac{4}{5}\right)\left(\frac{1}{m^1}\right)p^{11}$

Simplify

  $=-\frac{4p^{11}}{5m}$