Exponents worksheets help students move from repeated multiplication to the rules that make algebra work. These free printable exponents worksheets start with evaluating powers like 25, then cover the product, quotient and power rules, and finish with zero and negative exponents. Every PDF has an answer key, and the maker below builds fresh problems in seconds.
Quick answer: An exponent tells you how many times to multiply a base by itself: 25 = 2 × 2 × 2 × 2 × 2 = 32. To multiply powers with the same base, add the exponents; to divide, subtract them. This page has 6 free exponents worksheets (PDF) with answer keys for grades 6 to 8, plus a maker for new problems. Updated October 2026.
Ready-to-print samples
A few of the ready PDFs on this page. The full list is under Ready-to-print worksheets, and the maker above makes new problems on demand.
Evaluate powersLevel 1 with a full answer key.PDFProduct, quotient and power rulesLevel 2 with a full answer key.PDFZero and negative exponentsLevel 3 with a full answer key.PDFExponent rules (Set B)A second set of problems.PDF
What is an exponent?
An exponent is a small raised number that shows how many times the base is multiplied by itself. In 53, the base is 5 and the exponent is 3, so the value is 5 × 5 × 5 = 125. Exponents give a short way to write long products, and they are the basis of squares, cubes, area, volume and scientific notation.
Evaluating powers: worked examples
Each row writes the power as repeated multiplication and gives the value. Cover the last column and try each one first:
Base
Power
Repeated multiplication
Value
2
23
2 × 2 × 2
8
2
25
2 × 2 × 2 × 2 × 2
32
3
34
3 × 3 × 3 × 3
81
5
53
5 × 5 × 5
125
10
104
10 × 10 × 10 × 10
10,000
4
43
4 × 4 × 4
64
7
72
7 × 7
49
6
63
6 × 6 × 6
216
Laws of exponents worksheet: the six rules
The exponent rules save work when the base is the same. Learn the pattern, then check it with small numbers:
Rule
In words
Example
Result
Product
Same base: add the exponents
23 × 24
27 = 128
Quotient
Same base: subtract the exponents
56 ÷ 52
54 = 625
Power of a power
Multiply the exponents
(32)3
36 = 729
Zero exponent
Any non-zero number to the power 0 is 1
90
1
Negative exponent
Flip to the reciprocal
2-3
1/8
Power of a product
Apply the exponent to each factor
(2 × 3)2
22 × 32 = 36
Negative exponents worksheet: what do they mean?
A negative exponent does not make the number negative. It means take the reciprocal. Each step down in the exponent divides by the base, so 23 = 8, 22 = 4, 21 = 2, 20 = 1, 2-1 = 1/2. This pattern also shows why any non-zero number to the zero power is 1:
Expression
Reciprocal form
Value
2-1
1/21
1/2
2-2
1/22
1/4
3-2
1/32
1/9
5-3
1/53
1/125
10-3
1/103
1/1,000 = 0.001
(1/2)-3
23
8
Try ten powers and exponents problems
Use these as a warm-up. Write each power as repeated multiplication if you are stuck. Answers use commas for thousands.
#
Problem
Answer
1
26
64
2
33
27
3
54
625
4
105
100,000
5
44
256
6
62
36
7
93
729
8
210
1,024
9
73
343
10
82
64
Exponents vocabulary
Students answer questions faster when they know the words. These are the terms used on the worksheets and answer keys:
Word
Meaning
Example
Base
The number being multiplied
5 in 53
Exponent
How many times the base is used as a factor
3 in 53
Power
An expression with a base and an exponent
53
Square
A number to the power 2
62 = 36
Cube
A number to the power 3
43 = 64
Reciprocal
A number turned upside down
1/8 is the reciprocal of 8
Powers and exponents worksheet, practice and PDFs
This page is also searched as exponents worksheet, powers and exponents worksheet, exponent rules worksheet, zero exponent worksheet and evaluating exponents worksheet. All of them are the free PDFs above, with an answer key on the last page, for US Letter or A4, with no sign-up. Customize loads the same level into the maker for a fresh set of problems.
Write and evaluate numerical expressions with whole-number exponents
Grade 8
8.EE.A.1
Know and apply the properties of integer exponents
Grade 8
8.EE.A.3
Use numbers in scientific notation, which relies on powers of 10
Common mistakes with exponents
Mistake
Example
Fix
Multiplying the base by the exponent
23 = 6
Multiply the base by itself 3 times: 2 × 2 × 2 = 8
Multiplying exponents in the product rule
23 × 24 = 212
Add the exponents: 27
Treating a negative exponent as a negative number
2-3 = -8
It is a reciprocal: 1/8
Saying anything to the power 0 is 0
50 = 0
It is 1
Missing the parentheses
-32 = 9
The exponent applies to 3 only: -9. With parentheses, (-3)2 = 9
Real-life uses of exponents
Exponents describe anything that grows or shrinks by the same factor each step:
Situation
Power
Value
Area of a square with side 9 cm
92
81 cm²
Volume of a cube with side 5 in
53
125 in³
A message forwarded to 2 people, 10 times
210
1,024 people
Bacteria that double every hour, after 6 hours
26
64 times the start
Memory sizes: 210 bytes in a kilobyte
210
1,024
Which exponents worksheet should you start with?
Start with level 1 if students still write 23 as 6. Move to level 2 when powers come easily, and use Set B a week later for a retest.
Level
Skill
Best for
Level 1
Evaluate powers
Grade 6
Level 2
Product, quotient and power rules
Grade 8
Level 3
Zero and negative exponents
Grade 8
A weekly plan for exponents
Day
Focus
Suggested block
Monday
Evaluate powers
15 min
Tuesday
Product and quotient rules
15 min
Wednesday
Power of a power
15 min
Thursday
Zero and negative exponents
15 min
Weekly total
Four short sessions
60 min
Frequently asked questions
5 quick answers
Where can I download free exponents worksheets?
Open any worksheet in the Ready-to-print list on this page, choose US Letter or A4, then print or save the PDF. They are free, with answer keys, and no account is needed.
How do you evaluate an exponent?
Multiply the base by itself as many times as the exponent says. For example, 43 = 4 × 4 × 4 = 64.
What are the laws of exponents?
When the base is the same, add exponents to multiply, subtract them to divide, and multiply them for a power of a power. Any non-zero number to the power 0 is 1.
What is a negative exponent?
A negative exponent means the reciprocal. For example, 2-3 = 1/23 = 1/8.
What grade learns exponents?
Grade 6 evaluates whole-number exponents, and grade 8 learns the integer exponent rules.
