Powers · Divide — quotient rule · 4.2

With coefficients.

Divide the coefficients and subtract the exponents separately. 12x⁵ ÷ 3x² = (12÷3)x⁵⁻² = 4x³.

01 / THE IDEA

See it work.

Watch the method

With coefficients

12x⁵ ÷ 3x² = 4x³.

1 / 3
12x53x2\frac{12x^{5}}{3x^{2}}
1

Divide the coefficients

12 ÷ 3 = 4.

12÷3=412 \div 3 = 4
2

Subtract the exponents

Same base x — keep the base, subtract: 5 − 2.

x5÷x2=x3x^{5} \div x^{2} = x^{3}
3

Write the quotient

Same base when dividing → subtract exponents.

12x53x2=4x3\frac{12x^{5}}{3x^{2}} = 4 x^{3}
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.

Two jobs

Coefficients divide (numbers), exponents subtract (quotient rule).

Why it works

12÷3 = 4 out front; x⁵÷x² = x³.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Simplify 12y^2 ÷ 3y^1

1

Divide the coefficients

12 ÷ 3 = 4. 12 ÷ 3 = 4

2

Subtract the exponents

Same base y — keep the base, subtract: 2 − 1. y^2 ÷ y^1 = y^1

3

Write the quotient

Same base when dividing → subtract exponents. \frac12y^23y^1 = 4 y

EX 2medium

Simplify 8z^4 ÷ 4z^2

1

Divide the coefficients

8 ÷ 4 = 2. 8 ÷ 4 = 2

2

Subtract the exponents

Same base z — keep the base, subtract: 4 − 2. z^4 ÷ z^2 = z^2

3

Write the quotient

Same base when dividing → subtract exponents. \frac8z^44z^2 = 2 z^2

EX 3hard

Simplify 16x^4 ÷ 4x^2

1

Divide the coefficients

16 ÷ 4 = 4. 16 ÷ 4 = 4

2

Subtract the exponents

Same base x — keep the base, subtract: 4 − 2. x^4 ÷ x^2 = x^2

3

Write the quotient

Same base when dividing → subtract exponents. \frac16x^44x^2 = 4 x^2

04 / COMMON TRAPS

Where students slip.

Trap

Subtracting the coefficients.

Fix

Coefficients divide.

Trap

Dividing the exponents.

Fix

Exponents 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

Simplify 8z^3 ÷ 4z^2

Need a hint?
  • Divide the numbers in front.
  • Subtract the exponents.
C2

Simplify 8z^2 ÷ 2z^1

Need a hint?
  • Divide the numbers in front.
  • Subtract the exponents.
C3

Simplify 4x^5 ÷ 2x^2

Need a hint?
  • Divide the numbers in front.
  • Subtract the exponents.
C4

Simplify 12y^3 ÷ 4y^2

Need a hint?
  • Divide the numbers in front.
  • Subtract the exponents.
Apply

Apply (4)

A1

Simplify 8z^4 ÷ 2z^1

Need a hint?
  • Divide the numbers in front.
  • Subtract the exponents.
A2

Simplify 9z^4 ÷ 3z^1

Need a hint?
  • Divide the numbers in front.
  • Subtract the exponents.
A3

Simplify 6x^2 ÷ 2x^1

Need a hint?
  • Divide the numbers in front.
  • Subtract the exponents.
A4

Simplify 8x^5 ÷ 2x^2

Need a hint?
  • Divide the numbers in front.
  • Subtract the exponents.
Extension

Extension (4)

E1

Simplify 12x^2 ÷ 4x^1

Need a hint?
  • Divide the numbers in front.
  • Subtract the exponents.
E2

Simplify 8y^3 ÷ 4y^2

Need a hint?
  • Divide the numbers in front.
  • Subtract the exponents.
E3

Simplify 8y^3 ÷ 2y^1

Need a hint?
  • Divide the numbers in front.
  • Subtract the exponents.
E4

Simplify 16x^3 ÷ 4x^1

Need a hint?
  • Divide the numbers in front.
  • Subtract the exponents.