Powers · What is a power? · 1.1

Base and exponent.

A power like 3⁴ is repeated multiplication: the base (3) is multiplied by itself exponent-many times (4). 3⁴ = 3·3·3·3 = 81.

01 / THE IDEA

See it work.

Watch the method

Base and exponent

3⁴ means 3 multiplied 4 times = 81.

1 / 2
343^{4}
1

A power is repeated multiplication

3^4 means 3 multiplied 4 times.

3⋅3⋅3⋅33 \cdot 3 \cdot 3 \cdot 3
2

Multiply it out

Multiply the factors together.

=81= 81
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type with ^ for powers — e.g. x^5.

streak 0
best 0
… =
— / WHY IT WORKS

The idea underneath.

Base, exponent, value

The base is what is multiplied; the exponent says how many times. The result is the power’s value.

Why it works

2⁵ is five 2s multiplied: 32.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Evaluate 3^5

1

A power is repeated multiplication

3^5 means 3 multiplied 5 times. 3 · 3 · 3 · 3 · 3

2

Multiply it out

Multiply the factors together. = 243

EX 2medium

Evaluate 5^3

1

A power is repeated multiplication

5^3 means 5 multiplied 3 times. 5 · 5 · 5

2

Multiply it out

Multiply the factors together. = 125

EX 3hard

Evaluate 5^2

1

A power is repeated multiplication

5^2 means 5 multiplied 2 times. 5 · 5

2

Multiply it out

Multiply the factors together. = 25

04 / COMMON TRAPS

Where students slip.

Trap

Multiplying base × exponent (3·4 = 12).

Fix

3⁴ means 3·3·3·3 = 81, not 12.

Trap

Confusing 3⁴ with 4³.

Fix

The exponent is the small raised number.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Evaluate 4^3

Need a hint?
  • Multiply the base by itself exponent-many times.
  • Count the factors carefully.
C2

Evaluate 5^3

Need a hint?
  • Multiply the base by itself exponent-many times.
  • Count the factors carefully.
C3

Evaluate 10^2

Need a hint?
  • Multiply the base by itself exponent-many times.
  • Count the factors carefully.
C4

Evaluate 3^3

Need a hint?
  • Multiply the base by itself exponent-many times.
  • Count the factors carefully.
Apply

Apply (4)

A1

Evaluate 5^3

Need a hint?
  • Multiply the base by itself exponent-many times.
  • Count the factors carefully.
A2

Evaluate 10^3

Need a hint?
  • Multiply the base by itself exponent-many times.
  • Count the factors carefully.
A3

Evaluate 5^3

Need a hint?
  • Multiply the base by itself exponent-many times.
  • Count the factors carefully.
A4

Evaluate 4^2

Need a hint?
  • Multiply the base by itself exponent-many times.
  • Count the factors carefully.
Extension

Extension (4)

E1

Evaluate 4^3

Need a hint?
  • Multiply the base by itself exponent-many times.
  • Count the factors carefully.
E2

Evaluate 2^3

Need a hint?
  • Multiply the base by itself exponent-many times.
  • Count the factors carefully.
E3

Evaluate 5^2

Need a hint?
  • Multiply the base by itself exponent-many times.
  • Count the factors carefully.
E4

Evaluate 4^3

Need a hint?
  • Multiply the base by itself exponent-many times.
  • Count the factors carefully.