Chapter 4.4, Problem 32WE

To determine

To state:the number of positive factors of the given monomial.

Answer to Problem 32WE

The number of positive factors of $p^m{q}^m$ is ${(m+1)}^2$

Explanation of Solution

Given information:

p and q represent different prime numbers.

The given monomial:

  $p^m{q}^m$

As per the problem,

p and q represent different prime numbers.

To factorize $p^m{q}^m$ , ( $m+1$ ) powers of p ( $p^0,p^1,p^2,\mathrm{...},p^m$ ) can be multiplied with ( $m+1$ ) powers of q ( $q^0,q^1,q^2,\mathrm{...},q^m$ ) .

Thus, the number of positive factors of $p^m{q}^m$ is

  $(m+1)(m+1)={(m+1)}^2$ .