86 Chapter 1 Whole Numbers
a. Read as “7 to the second power” or “7 squared.” The base is 7 and
the exponent is 2. Write the base as a factor 2 times.
Multiply.
b. Read as “2 to the 5th power.” The base is 2 and the
exponent is 5. Write the base as a factor 5 times.
Multiply, working left to right.c. Read as “10 to the 4th power.” The base is 10 and
the exponent is 4. Write the base as a factor 4 times.
Multiply, working left to right.d. 61 6 Read 61 as “6 to the first power.” Write the base 6 once.10,000
1,000 10
100 10 10
104 10 10 10 10 104
32
16 2
8 2 2
4 2 2 2
25 2 2 2 2 2 25
49
72 7 7 72
Caution! Note that means It does not mean That is,
25 32 and 2 5 10.25 2 2 2 2 2. 2 5.
EXAMPLE (^9) The prime factorization of a number is What is the
number?
StrategyTo find the number, we will evaluate each exponential expression and
then do the multiplication.
WHYThe exponential expressions must be evaluated first.
Solution
We can write the steps of the solutions in horizontal form.
Evaluate the exponential expressions:
and
Multiply, working left to right.
3,240 Multiply.
648 5
34 81.23 34 5 8 81 5 23 8
23 34 5.
Self Check 9
The prime factorization of a
number is What is the
number?
Now TryProblems 93 and 972 33 52.
23 34 5 is the prime factorization of 3,240.Using Your CALCULATOR The Exponential Key:
Bacteria Growth
At the end of 1 hour, a culture contains two bacteria.
Suppose the number of bacteria doubles every hour
thereafter. Use exponents to determine how many
bacteria the culture will contain after 24 hours.
We can use a table to help model the situation. From
the table, we see a pattern developing: The number
of bacteria in the culture after 24 hours will be 2^24.Number of
Time bacteria
1 hr
2 hr
3 hr
4 hr
24 hr ? 22416 248 234 222 2162
44
8
5
3,24081
8
648Success Tip Calculations that you cannot perform in your head should be
shown outside the steps of your solution.