A square floor has 4 tiles across and 4 tiles down. Instead of writing 4 × 4, we can write 4². Both expressions equal 16 tiles.
← Pattern PathwayLesson 2 of 7
Algebra 1 · Unit 1 · Micro-Lesson 2
Understand Exponents
I canwrite repeated multiplication using an exponent and explain what the exponent means.
PATHWAY2of 7
Why should I care?
Connect the Math to Real Life
Exponents give us a short way to write repeated multiplication. They appear in area, computer storage, science, finance, and game growth.
Important words
Build the Vocabulary
Read the meaning, then connect it to the example.
Base
The larger number that is used again and again in the multiplication.
ExampleIn 5³, the base is 5: 5 × 5 × 5.
Exponent
The small raised number. It tells how many times to use the base as a factor.
ExampleIn 5³, the exponent is 3 because there are three 5s.
Power
The complete expression that includes a base and an exponent.
Example5³ is a power. It is read as ‘five cubed.’
Start with something you can see
Build a Power
Move the controls. Watch the picture, repeated multiplication, exponent, and total change together.
SQUARE BUILDER
Equal rows and columns
A square uses the same number across and down.
4 × 4=42=16
Squared means the same number is used as a factor 2 times. It can model the area of a square.
CUBE BUILDER
See All Three Dimensions
The picture separates the cube into three layers. Each layer contains 3 rows of 3 cubes.
Length3 cubes×Width3 cubes×Height3 cubes=Total27 cubes
3 × 3 × 3=33=27 cubes
2 × 2 × 223 = 83 × 3 × 333 = 274 × 4 × 443 = 64
Cubed means the same number is used as a factor three times: length, width, and height.
Read every part
What Does an Exponent Tell Us?
The exponent is a counting instruction: it counts how many times the base is used as a factor.
5base3exponent5³power
53 does not mean 5 × 3.It means 5 × 5 × 5 = 125.
Use the base 5 three times. The exponent is not a number you multiply by the base.
Connect it to movies
What Is the Difference Between 2D and 3D?
2D stays flat on the screen
A flat shape has two dimensions: length and width.
4 units long×4 units wide=42 = 16 square units
3D gives the appearance of depth
A solid object has three dimensions: length, width, and height.
3 long×3 wide×3 high=33 = 27 cubes
Important: “3D” and “cubed” are connected because both involve three dimensions. The exponent 3 means the same measurement is multiplied three times.
Pause and check
Can You Read the Pattern?
Which expression means 6 × 6 × 6?
What does 4² mean?
Can 8 × 4 × 3 be written as 8³?
Choose a job challenge
Where Would I Use This?
Exponents help workers describe equal measurements and large repeated products quickly.
JOB CARD
Tile the Floor
A square display floor has 6 tiles in each row and 6 rows.
🧑🔧
6 tiles × 6 tiles
What repeats?Two equal sides→Repeated multiplication6 × 6→Exponent form6²→Total36 tiles
Beyond boxes and floors
Powers Show Up Everywhere
Here are specific examples of why people use exponent notation.
Climate Science
A scientist may estimate 40,000,000,000,000,000,000 carbon-dioxide molecules in a tiny air sample. Scientific notation makes that easier to write and compare: 4 × 1019.
Photos and Videos on Your Phone
A phone with about 27 = 128 GB of storage may hold tens of thousands of photos. Longer, higher-quality videos use more storage, so the same phone holds fewer videos than photos.
🖼️🖼️🖼️🎬128 GB
Small Savings Can Become Big Money
Start with $100. A 10% gain means multiply by 1.10 each year.
Start$100.00× 1.10Year 1$110.00× 1.10Year 2$121.00× 1.10Year 3$133.10
The shortcut is $100 × (1.10)3 = $133.10. The exponent 3 means the growth happens three times.
Could $1 a day make you a millionaire?
Not by itself—but starting young still matters. If someone invested $1 every day from age 15 to 65 and averaged an 8% yearly return, the account could grow to about $241,000. About $4.15 per day under the same assumptions could grow to roughly $1 million.
This is a mathematical illustration, not a guarantee. Actual investment returns, fees, and taxes vary.Video-Game Choices
If a player has 3 choices at each of 4 stages, there can be 3 × 3 × 3 × 3 = 34 = 81 different paths.
Try it yourself
8-Question Practice
Choose an answer, check your thinking, and use the hint if you need another try.