Introduction to Exponents

Show your work for each problem.

1.
What does mean?
1. a)
2. b)
3. c)
4. d)
Answer:
means 2 multiplied by itself 4 times: . The exponent (4) tells us how many 2s to multiply.
2.
Calculate
Answer: 25
. The exponent 2 means we multiply 5 by itself once.
3.
In the expression , what is the base?
1. a)3
2. b)7
3. c)343
4. d)21
Answer: 7
In , the base is 7 (the number being multiplied) and the exponent is 3 (how many times to multiply).
4.
Calculate
Answer: 8
. First , then .
5.
Calculate
Answer: 16
1. What is the base in ? 4
2. What is the exponent? 2
3. What is ? 16
6.
Calculate
Answer: 81
7.
Which is greater: or ?
1. a)
2. b)
3. c)Cannot determine
4. d)They are equal
Answer:
and . Since , is greater. Don't assume the larger base always wins!
8.
Write using an exponent, then calculate.
Answer: 7776
1. What number is being repeated? 6
2. How many times is 6 multiplied? 5
3. Write in exponential form: 5
4. Calculate 7776
9.
What is ?
Answer: 10000
(1 followed by 4 zeros). This is ten thousand.
10.
Calculate
Answer: 64
1. What is ? 4
2. What is ? 8
3. What is ? 16
4. What is ? 32
5. What is ? 64
11.
What is for any number n?
1. a)0
2. b)1
3. c)n
4. d)n + 1
Answer: n
Any number to the power of 1 equals itself. , , .
12.
Calculate
Answer: 625
13.
A cube has sides of 6 cm. What is its volume?
Answer: 216
1. What formula do we use for volume of a cube? side cubed
2. What is the side length? 6
3. Write in exponential form: Volume = ? 6^3
4. Calculate 216
14.
Which is the correct way to read ?
1. a)Four times five
2. b)Five fours
3. c)Four to the fifth power
4. d)Five to the fourth power
Answer: Four to the fifth power
is read as 'four to the fifth power' - the base (4) is raised to the exponent (5).
15.
A bacterium doubles every hour. Starting with 1, how many are there after 5 hours?
Answer: 32
1. After 1 hour, how many bacteria? 2
2. After 2 hours? 4
3. After 3 hours? 8
4. After 4 hours? 16
5. After 5 hours? (This is ) 32
16.
What is ? (This is 1 kilobyte in bytes)
Answer: 1024
. This is why 1 KB = 1024 bytes in computing!
17.
A square has area 64 square cm. What is the side length?
Answer: 8
1. Area of square = side squared. If Area = 64, then side = ? 8
2. Verify: What is ? 64