Properties of Exponents

Negative Exponents

100

x^-4

1/x⁴

200

3/x^-6

3x⁶

300

-2y^-4 (y⁷)

-2y³

400

(d³n²)^-5 (d⁷n^-4)

1/d⁸n¹⁴

500

(b^-2/x³)^-3

b⁶x⁹

Power of a Product

100

(ab⁵)²

a²b¹⁰

200

(5c⁴k³)²

25c⁸k⁶

300

6mz³ (3m³z⁴)³

162m¹⁰z¹⁵

400

(t⁴s⁶)⁹ (4g⁵ts⁵)²

16g¹⁰t³⁸s⁶⁴

500

(12x⁹h⁴k⁶y)² (4x³h²ky⁵)^-2

9x¹²h⁴k¹⁰ / y⁸

Dividing Powers

100

x⁵ / x²

x³

200

y⁸z¹⁴ / y⁶z¹¹

y²z³

300

15w¹¹xy⁴ / -5w⁵x⁵y⁵

-3w⁶ / x⁴y

400

6a³b¹⁴c⁸d⁸ / 24a⁴b⁶c²d¹²

b⁸c⁶ / 4ad⁴

500

1 / e⁴f⁸gh¹² (9e⁷f³g⁵h⁹)^-1

9e³g⁴ / f⁵h³

Power of a Quotient

100

(x⁴/y⁶)²

x⁸/y¹²

200

(4/h³j⁵)²

16/h⁶j¹⁰

300

(2a⁴b³/c⁶d¹⁰)³

8a¹²b⁹/c¹⁸d³⁰

400

(1/6x³y⁷z⁹)^-1 (-2x⁹y²z⁶)^-4

3 / 8x³³yz¹⁵

500

(4j⁵k^-2mn³/8j^-6k³m^-4n²)^-2

4k¹⁰/j²²m¹⁰n²