Exponents & Scientific Notation — Practice
An exponent counts how many times you multiply, not what you multiply by. That one idea explains every rule.
What these questions cover
These questions use 5 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Base — The number being multiplied. In 53 the base is 5.
- Exponent — How many times the base is used as a factor. In 53 the exponent is 3.
- Power — The whole expression, 53, and also its value, 125.
- Scientific notation — A number written as a × 10n, where 1 ≤ a < 10.
- Standard form — The ordinary way of writing a number, like 47,000.
Problem 1
Evaluate 34.
Worked answer
81
3 × 3 × 3 × 3 = 81
Problem 2
Evaluate 25.
Worked answer
32
2 × 2 × 2 × 2 × 2 = 32
Problem 3
Evaluate 70.
Worked answer
1
Follow the pattern down: 72 = 49, 71 = 7, 70 = 1.
Problem 4
Simplify 52 · 53 and give its value.
Worked answer
3125
52+3 = 55
= 3125
Problem 5
Write 4.3 × 106 in standard form.
Worked answer
4300000
4.3 × 1,000,000 = 4,300,000
Problem 6
Simplify 23 · 24 and give its value.
Worked answer
128
23+4 = 27
= 128
Problem 7
Simplify 3835 and give its value.
Worked answer
27
38-5 = 33
= 27
Problem 8
Simplify (23)2 and give its value.
Worked answer
64
23 × 2 = 26
= 64
Problem 9
Evaluate 2-3.
Worked answer
1/8
2-3 = 123
= 18
Problem 10
Write 0.00047 in scientific notation. Enter just the exponent of 10.
Worked answer
-4
0.00047 → 4.7 is 4 places right
Small number, so negative: 4.7 × 10-4
Problem 11
Write 52,000 in scientific notation. Enter just the exponent of 10.
Worked answer
4
52,000 → 5.2 is 4 places left
5.2 × 104
Problem 12
Compute (3 × 105)(2 × 10-2) and give the answer in standard form.
Worked answer
6000
3 × 2 = 6
105 · 10-2 = 103
6 × 103 = 6000
Problem 13
Simplify (23)2 · 2425 and give its value.
Worked answer
32
(23)2 = 26
Top: 26 · 24 = 210
21025 = 25 = 32
Problem 14
Compute (5 × 104)(4 × 103) in scientific notation. Enter just the exponent of 10.
Worked answer
8
5 × 4 = 20 and 104 · 103 = 107
20 × 107 = 2 × 101 × 107
= 2 × 108
Problem 15
Which is larger, 210 or 103?
- 210
- 103
- They are equal
Worked answer
210
210 = 1024
103 = 1000
1024 > 1000
Problem 16
Evaluate (-2)4 + (-2)3.
Worked answer
8
(-2)4 = 16 — four negatives, even
(-2)3 = -8 — three negatives, odd
16 + (-8) = 8