Example 1
Write 5 × 5 × 5 in exponential form.
- Identify the repeating factor: 5.
- Count how many times it repeats: 3 times.
- Write base as 5 and exponent as 3.
Answer: 5³
📗 Class 7 maths · session 11 of 12 · 60 minutes · 🎁 free with an account
Exponents and powers
Welcome back to the superhero math academy! I am Captain Calc, and today we unleash the super-powers of exponents to handle huge numbers with ease.
🤖 Written with Google's Gemini AI. A second AI solved all 54 questions without seeing the answers, and both agree. One of our teachers has not read it yet, so if something looks wrong, please tell us.
A complete lesson · 60 minutes
Teach it, see it, practise it, all on this page.
Open this page with your learner and work down it, or press Teach this lesson to go through it one step at a time on a big screen. Every section has something to do.
- Warm-up3 min
- Warm-up games5 min
- Introduction to Base and Exponent8 min
- Multiplying and Dividing Powers with the Same Base7 min
- Power of a Power and Zero Exponent7 min
- Expressing Large Numbers in Standard Form7 min
- Power Up Decoder6 min
- Prime Base Builder5 min
- Cosmic Standard Form Mission6 min
- Quiz5 min
- Set the project1 min
By the end you can
- Identify the base and exponent in any exponential expression.
- Apply laws of exponents to simplify multiplication and division of powers.
- Evaluate expressions involving zero exponent and power of a power.
- Express very large numbers in standard form using powers of 10.
Before you start
- Basic operations on integers like multiplication and division.
- Concept of prime factorisation of numbers.
Have ready
- Grid paper or notebook and a pencil.
- Colored markers or pens for tracking power rules.
Class 7 · CBSE, ICSE and state boards
Warm-up · think first
A super-virus doubles every hour. If there is 1 virus now, how many viruses will there be after 4 hours?
Show the answer
16 viruses. At 0 hour there is 1. After 1 hour there are 2. After 2 hours there are 4. After 3 hours there are 8. After 4 hours there are 16. This is 2⁴.
Teacher tip: Ask students if they noticed a pattern of multiplying 2 repeatedly.
🎮 Warm-up games · 5 quick games
Play with Captain Calc
Six minutes with Captain Calc. Vote, say why, then show the answer.
- Which one does not belong: 2⁴, 4², 16, 23? (2⁴ · 4² · 16 · 23)
Answer: 23 does not belong. 2⁴ = 16, 4² = 16, and 16 is their numerical value, but 23 is not equal to 16. - Would you rather receive ₹2⁵ every day for a week or ₹100 every day for a week? (₹2⁵ per day · ₹100 per day)
Answer: ₹100 per day gives more money. ₹2⁵ is ₹32 per day (total ₹224), while ₹100 per day gives ₹700 in total. - Any non-zero number raised to the power 0 is equal to 1. (Always · Sometimes · Never)
Answer: Always. By the division law of exponents, aⁿ ÷ aⁿ = aⁿ⁻ⁿ = a⁰, which also equals a ÷ a = 1 for any non-zero number a. - I am a power of 3. My exponent is 3. What number am I?
Answer: 27. Here the base is 3 and exponent is 3, so 3³ = 3 × 3 × 3 = 27. - Why do scientists use exponents when writing about space or tiny atoms?
Answer: Space distances are huge and atom sizes are tiny. Writing many zeros takes time and causes errors. Exponents make writing giant or tiny numbers fast and simple.
Part 1 of 4 · learn, see, practise
Introduction to Base and Exponent
When a number is multiplied by itself repeatedly, we use exponents for short.
In 2⁴, 2 is called the base and 4 is called the exponent or index or power.
The expression 2⁴ is read as 2 raised to the power 4, which means 2 × 2 × 2 × 2 = 16.
Example 2
Find the value of 3⁴.
- Write 3⁴ as repeated multiplication: 3 × 3 × 3 × 3.
- Multiply step-by-step: 3 × 3 = 9, 9 × 3 = 27, 27 × 3 = 81.
Answer: 81
Practise it
Start with the warm-up and go as far as you can. The stretch questions are meant to be hard.
Warm-up
Warm-up
Core
Core
Stretch 🔥
Stretch 🔥
Answers (for the teacher)
- 7
- 32
- 2⁶
- -27
- 2² × 3³
- 3²
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Unlocking the rest of this lesson gives you:
- Part 2: Multiplying and Dividing Powers with the Same Base, with practice at three levels
- Part 3: Power of a Power and Zero Exponent, with practice at three levels
- Part 4: Expressing Large Numbers in Standard Form, with practice at three levels
- Class activity 1: Power Up Decoder
- Class activity 2: Prime Base Builder
- Class activity 3: Cosmic Standard Form Mission
- A 10-question quiz
- After-class project: The Solar System Exponent File
- Homework and a printable practice sheet with answers
- Teach mode and the minute-by-minute teacher's plan
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FAQ
Exponents and powers: questions
Why are exponents useful in real life?
Exponents help us write and calculate extremely large or small numbers quickly, such as computer storage sizes, bacterial growth, and distances in space.
Is 0⁰ equal to 1?
In Class 7 math, zero raised to power zero is considered undefined; our rule a⁰ = 1 applies to any non-zero number a.
What is the difference between square and cube of a number?
A square has an exponent of 2 (multiplying a number by itself), while a cube has an exponent of 3 (multiplying a number by itself twice).
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