Exponents for kids

What kids learn about exponents, grade by grade

• Grade 5 (5.NBT.A.2): powers of 10 written with exponents, like 10³ = 1,000, and what happens to digits when you multiply by them.
• Grade 6 (6.EE.A.1, 6.EE.A.2c): write and work out expressions like 4³ and 2⁵, and use exponents in the order of operations.
• Grade 8 (8.EE.A.1 to 8.EE.A.4): the exponent rules, zero and negative exponents, square and cube roots, and scientific notation for very big and very small numbers.

Where to start with exponents

Start with what an exponent means, using squares and cubes children can picture. Then powers of 10. Only after that move to the rules: a child who can write out 2³ × 2⁴ in full will never need to memorize “add the exponents”.

The big idea behind exponents

An exponent is shorthand for repeated multiplication, the way multiplication is shorthand for repeated addition. In 5³, 5 is the base and 3 is the exponent (or power). It means 5 × 5 × 5 = 125.

The second and third powers have special names because they describe real shapes: a number squared is the area of a square, and a number cubed is the volume of a cube.

Powers of 10

Powers of 10 are where most children first meet exponents. The exponent tells you how many zeros follow the 1, and negative powers of 10 give the decimal places.

Power	Number	Name
10⁰	1	one
10¹	10	ten
10²	100	hundred
10³	1,000	thousand
10⁴	10,000	ten thousand
10⁵	100,000	hundred thousand
10⁶	1,000,000	million
10⁻¹	0.1	tenth
10⁻²	0.01	hundredth

This is why scientific notation works: the distance to the Sun, about 150,000,000 km, is 1.5 × 10⁸ km.

The exponent rules (grade 8)

Every rule comes straight from writing the powers out in full. Show the long version once and the rule makes sense.

Rule	Example	Why
Multiply: add the exponents	2³ × 2⁴ = 2⁷	(2·2·2)(2·2·2·2) is seven 2s
Divide: subtract the exponents	5⁶ ÷ 5² = 5⁴	Two 5s on the bottom cancel two on top
Power of a power: multiply	(3²)⁴ = 3⁸	Four lots of 3²: 2 + 2 + 2 + 2 = 8
Zero exponent	7⁰ = 1	7³ ÷ 7³ = 1 and also 7⁰
Negative exponent	10⁻² = 1/100	Keep dividing by 10 below 10⁰

The rules only work when the bases are the same. 2³ × 3⁴ can’t be combined into one power.

Where kids get stuck with exponents

How to teach exponents at home

Fold a sheet of paper

Fold a sheet in half again and again, counting layers: 2, 4, 8, 16, 32. Each fold is one more power of 2. Most people can’t get past 7 folds, which is 2⁷ = 128 layers.

Build squares and cubes

Use sugar cubes, blocks or Lego. Build 2², 3² and 4² as flat squares, then 2³ and 3³ as cubes. Children see why “squared” and “cubed” have those names.

Tell the rice and chessboard story

One grain of rice on the first square, 2 on the next, 4, 8 and so on. By the last square it is 2⁶³ grains, more rice than has ever been grown. It shows how fast powers grow.

Count zeros

Say a power of 10 and have your child write it: 10⁴, 10⁶. Then go backwards: “1,000,000 is 10 to the what?”

Exponents worksheets

Printable PDFs with answer keys. The first one has its own page with tips: exponents worksheet.

• Exponents, squares and cubesGrade 6 · 50 questions + key
• Exponent rulesGrade 8 · 50 questions + key
• Order of operations with exponentsGrades 6–8 · 50 questions + key
• Scientific notationGrade 8 · 50 questions + key
• Scientific notation operationsGrade 8 · 50 questions + key
• Multiply and divide by 10, 100, 1000Grades 3–5 · powers of 10

Make a fresh exponents test · Make an exponent rules test · Make a scientific notation test

Exponents charts and related lessons

• Multiplication chart: the perfect squares run down its diagonal.
• Place value chart: see what multiplying by powers of 10 does to each digit.
• Multiplying by 10, 100 and 1000 · Order of operations · 8th grade math