Concept 7 of 9
Orders: The Power of Powers
Today's big idea
An exponent tells you how many times to multiply the base by itself.
A power counts copies of the base, so 9² means two nines and not 9 × 2.
How it works
👀 What's going on?
Writing 2 × 2 × 2 × 2 × 2 × 2 takes a while, and it is easy to lose count. A power says the same thing in two characters.
💡 Here's the trick
Look at the power above. The large digit is the base and the small raised digit is the exponent. The exponent counts how many copies of the base get multiplied, so 2⁶ means six twos.
🪄 How to do it
- 1.Read the power above as a base and an exponent.
- 2.Write the base out that many times, joined by multiply signs.
- 3.Work through the multiplying to reach the value.
✍️ Try it
What is 4³? Then: what is 10 + 2 × 3²?
Three copies of 4 give 4 × 4 × 4, which is 64. In the second, 3² is 9, then 2 × 9 = 18, so the total is 28.
⚠️ Watch out
You might be thinking 7³ means 7 × 3. It means 7 × 7 × 7 instead, which is 343. The small digit counts the copies, and it never joins in as one of them.
🌟 Why this matters
Squares tell you the area of a square room, and cubes tell you the space inside a box. Powers also describe how quickly a rumour spreads.
Exam tip: Turn every power into its plain value before you touch the rest of the sum.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“What is 3⁴?”
- 1
Read the power
3⁴ means 3 multiplied by itself 4 times. ⚡
- 2
Expand
3 × 3 × 3 × 3
- 3
Multiply in pairs
3 × 3 = 9. 9 × 3 = 27. 27 × 3 = 81.
- 4
Answer ✓
3⁴ = 81
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
A power is repeated multiplication. Expand it first, then multiply it out.
POWER · ROUND 1 OF 3
2⁵
Quick check
✅ VERIFICATION
What is the value of 5³?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Operator Families
Same family? Solve left to right.