Question

Factor each monomial completely.

$-\mathbf{20}{m}^5{n}^2$

Short answer

$-\mathbf{1}\cdot \mathbf{2}\cdot \mathbf{2}\cdot \mathbf{5}\cdot m\cdot m\cdot m\cdot m\cdot m\cdot n\cdot n$

Step-by-step solution

Step 1. Define monomial.

Monomial can be expressed as a product of prime numbers and variables, and no variable has an exponent greater than 1.

Step 2. Factor given number.

Factor given number and write all powers of variables as products.

$$\begin{gathered} -20m^5{n}^2=-1\cdot 20m^5{n}^2 \\ =-1\cdot 2\cdot 10\cdot m\cdot m\cdot m\cdot m\cdot m\cdot n\cdot n \\ =-1\cdot 2\cdot 2\cdot 5\cdot m\cdot m\cdot m\cdot m\cdot m\cdot n\cdot n \end{gathered}$$

Step 3. Write the conclusion.

The given monomial cannot be factored further, therefore$-1\cdot 2\cdot 2\cdot 5\cdot m\cdot m\cdot m\cdot m\cdot m\cdot n\cdot n$ is the required answer.