Powers · Divide — quotient rule · 4.3

Numbers, same base.

The quotient rule works for numeric bases: 2⁷ ÷ 2⁴ = 2⁷⁻⁴ = 2³ = 8. Keep the base, subtract the exponents, then evaluate.

01 / THE IDEA

See it work.

Watch the method

Numbers, same base

2⁷ ÷ 2⁴ = 2³ = 8.

1 / 2
2724\frac{2^{7}}{2^{4}}
1

Same base — subtract the exponents

Keep the base (2, subtract 7 − 4.

(27÷(24=(23(2^{7} \div (2^{4} = (2^{3}
2

Evaluate

Now compute the power.

(23=8(2^{3} = 8
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type with ^ for powers — e.g. x^5.

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— / WHY IT WORKS

The idea underneath.

Same idea, numbers

Equal bases divide by subtracting exponents; then evaluate the single power.

Why it works

128 ÷ 16 = 8 = 2³.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Evaluate 3^5 ÷ 3^2

1

Same base — subtract the exponents

Keep the base (3, subtract 5 − 2. (3^5 ÷ (3^2 = (3^3

2

Evaluate

Now compute the power. (3^3 = 27

EX 2medium

Evaluate 3^4 ÷ 3^2

1

Same base — subtract the exponents

Keep the base (3, subtract 4 − 2. (3^4 ÷ (3^2 = (3^2

2

Evaluate

Now compute the power. (3^2 = 9

EX 3hard

Evaluate 5^4 ÷ 5^2

1

Same base — subtract the exponents

Keep the base (5, subtract 4 − 2. (5^4 ÷ (5^2 = (5^2

2

Evaluate

Now compute the power. (5^2 = 25

04 / COMMON TRAPS

Where students slip.

Trap

Dividing the bases.

Fix

Keep the base; subtract exponents.

Trap

Dividing the exponents.

Fix

They subtract.

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 3^4 ÷ 3^1

Need a hint?
  • Keep the base; subtract the exponents.
  • Then evaluate.
C2

Evaluate 5^4 ÷ 5^1

Need a hint?
  • Keep the base; subtract the exponents.
  • Then evaluate.
C3

Evaluate 3^2 ÷ 3^1

Need a hint?
  • Keep the base; subtract the exponents.
  • Then evaluate.
C4

Evaluate 2^2 ÷ 2^1

Need a hint?
  • Keep the base; subtract the exponents.
  • Then evaluate.
Apply

Apply (4)

A1

Evaluate 2^3 ÷ 2^1

Need a hint?
  • Keep the base; subtract the exponents.
  • Then evaluate.
A2

Evaluate 3^5 ÷ 3^2

Need a hint?
  • Keep the base; subtract the exponents.
  • Then evaluate.
A3

Evaluate 3^5 ÷ 3^2

Need a hint?
  • Keep the base; subtract the exponents.
  • Then evaluate.
A4

Evaluate 2^5 ÷ 2^2

Need a hint?
  • Keep the base; subtract the exponents.
  • Then evaluate.
Extension

Extension (4)

E1

Evaluate 3^4 ÷ 3^1

Need a hint?
  • Keep the base; subtract the exponents.
  • Then evaluate.
E2

Evaluate 2^3 ÷ 2^2

Need a hint?
  • Keep the base; subtract the exponents.
  • Then evaluate.
E3

Evaluate 3^4 ÷ 3^1

Need a hint?
  • Keep the base; subtract the exponents.
  • Then evaluate.
E4

Evaluate 3^5 ÷ 3^2

Need a hint?
  • Keep the base; subtract the exponents.
  • Then evaluate.