## Multiplying Integers

## Work Time

# Multiplying Integers

Identify and use patterns in the table to help you evaluate the expressions.

Use your results to help you complete the following statements.

- The product of two numbers with the same sign is
.*_**_**_**_* - The product of two numbers with different signs is
.*_**_**_**_*_

# Challenge Problem

Recall that the notation ${a}^{m}$ means to multiply *m* instances of *a*.

Example: ${2}^{4}$ = 2 ⋅ 2 ⋅ 2 ⋅ 2

The expression ${(-a)}^{m}$ means to multiply *m* instances of the opposite of *a* (that is, *m* instances of *–a* ). The notation ${-a}^{m}$ means to multiply *m* instances of *a* and then find the opposite of the result.

- Find the value of each expression.
- $-{2}^{4}$ =
- ${(-2)}^{3}$ =
- $-{(-7)}^{2}$ =
- ${5}^{3}$ =

- Suppose
*p*is a positive integer. For what values of*m*does $-{p}^{m}={(-p)}^{m}$? - Suppose
*n*is a negative integer. For what values of*m*does $-{n}^{m}={(-n)}^{m}$?

## Hint:

- What happens to the products as the first factor decreases by 1?
- How does the product compare to the product you would get if the factor was positive?