Basic Mathematics for College Students

2.4 Multiplying Integers 171

EXAMPLE (^7) Evaluate:
StrategyWe will rewrite the expression as a product of repeated factors, and then
perform the multiplication. We must be careful when identifying the base. It is 2,
not.
WHYSince there are no parentheses around , the base is 2.
Solution
Read as “the opposite of the square of two.”
Do the multiplication within the parentheses to get 4.
Then write the opposite of that result.

 4

 22 (22)

 2

 2

 22

Self Check 7

Evaluate:

Now TryProblem 71

 42

Using Your CALCULATOR Raising a Negative Number to a Power

We can find powers of negative integers, such as , using a calculator. The

keystrokes that are used to evaluate such expressions vary from model to

model, as shown below. You will need to determine which keystrokes produce

the positive result that we would expect when raising a negative number to an

even power.

56 Some calculators don’t require the parentheses

to be entered.

56 Other calculators require the parentheses to be

entered.

56

From the calculator display, we see that (5)^6 15,625.

( () ) ^ ENTER 15625

( / ) yx 

/ yx 

(5)^6



5 Solve application problems by multiplying integers.

Problems that involve repeated addition are often more easily solved using
multiplication.

EXAMPLE (^8) Oceanography
Scientists lowered an underwater vessel called
a submersibleinto the Pacific Ocean to record
the water temperature. The first measurement
was made 75 feet below sea level, and more
were made every 75 feet until it reached the
ocean floor. Find the depth of the submersible
when the 25th measurement was made.
Analyze

• The first measurement was made 75 feet below sea level. Given


• More measurements were made every 75 feet. Given


• Find the depth of the submersible when it made the 25th
  measurement. Find

Form If we use negative numbers to represent the depths at which the
measurements were made, then the first was at feet. The depth (in feet) of the
submersible when the 25th measurement was made can be found by adding
twenty-five times. This repeated addition can be calculated more simply by
multiplication.

 75

 75

Emory Kristof/NationalGeographic/Getty Images

Self Check 8

GASOLINE LEAKSTo determine

how badly a gasoline tank was

leaking, inspectors used a drilling

process to take soil samples

nearby. The first sample was

taken 6 feet below ground level,

and more were taken every 6 feet

after that. The 14th sample was

the first one that did not show

signs of gasoline. How far below

ground level was that?

Now TryProblem 97