Laws of Exponents

Product Rule

100

x²∙x³

What is x⁵

200

x ∙x⁵

What is x⁶

300

(5a²b)(a^-6b)

What is 5a^-4b² or 5b²/a⁴

400

(2a⁷)(-3a²)

What is -6a⁹

500

(-3b⁹)(-b)

What is 3b¹⁰

Quotient Rule

100

x/x

What is 1

200

x⁵/x²

What is x³

300

x³y / xy²

What is x² / y

400

6ab / 3ab²

What is 2/b

500

15a^-3b⁶ / 12a³b³

What is 5a^-6b³ / 4 or 5b³ / 4a⁶

Power Rule

100

(a⁴)³

What is a¹²

200

(ab³)⁵

What is a⁵b¹⁵

300

(2a³g²)⁵

What is 2⁵a¹⁵g¹⁰ or 64a¹⁵g¹⁰

400

(3a³b^-4)⁴

What is 3⁴a¹²b^-16 or 81a¹² / b¹⁶

500

(7ab^-2c⁴)²

What is 49a²b^-4c⁸ or 49a²c⁸ / b⁴

Negative Exponents

100

x^-1

What is 1/x

200

2x^-2

What is 2 / x²

300

x^-4y^-2 / xy²

What is 1 / x⁵y⁴

400

6x^-6h³ / h^-2

What is 6h⁵ / x⁶

500

-3x⁴y^-6 / x^-2

What is -3x⁶ / y⁶

Mixed Bag

100

(3a)³

What is 27a³

200

3m^-4 / m³

What is 3 / m⁷

300

(3x³)(-5x²)³

What is -375x⁹

400

16x⁵/4x³

What is 4x²

500

3x³y^-1z^-1 / x^-4y⁰z¹

What is 3x⁷ / yz²