Exponent Rules

Add / Subtract

100

10x - 13x

-3x

200

-xyz⁵ + 2xyz⁵

xyz⁵

300

3x²y - 9x²y

-6x²y

400

-15wq - 3wq + 8 wq

-10wq

500

4mn⁴ - 8mn + 6mn⁴

10mn⁴ - 8mn

Product Rule

100

(3x⁵)(-6x²)

-18x⁷

200

(-4x²yz⁸)(-x⁴yz)

4x⁶y²z⁹

300

(-2n³p⁵)(np)(-4n²p)

8n⁶p⁷

400

(-1/3 x⁶y) (27xy)

-9x⁷y²

500

A rectangular garden has a length of 12x²y⁴z and a width of 5/4xy²z⁴ ; find the area of the garden

15x³y⁶z⁵

Power of a Power

100

(2x²)³

8x⁵

200

(4y²z³)⁴

256y⁸z¹²

300

(3x⁶yz²)²

9x¹²y²z⁴

400

(-1/2 x³y⁶)⁵

-1/32x¹⁵y³⁰

500

(-2/3 x⁴y³)⁴

1/5x¹⁶y¹²

Quotient Rule

100

When dividing monomials what do you do with the exponents?

Subtract

200

x⁸/x⁴

x⁴

300

9x⁵y / 3xy

3x⁴

400

5x⁷y²z⁴ / 20x⁵yz

x²y¹z³ / 5

500

-4c¹⁴d⁷ / 16c³d⁷

- c¹¹ / 4

Mixed Practice

300

A square has a side length of 3y⁵ 

What is the area of the square? 

9y¹⁰

400

9a⁷b(3a⁶b²) / 18a⁵b³

3a⁸ / 2

500

The area of a rectangle is 20a⁵b³, and the length is 4a²b What is the width? 

5a³b²