Exponent Rules

Product Rule

100

x^3 * x^6

x^9

200

2x^5 * x^7

2x^12

300

(4f^8)(6f^4)

24f^12

400

(n³)^-2・2n³

2/(n^3)

500

(-2r^4y^7)(3r^6)^3

-54r²²y⁷

600

(7s^5p^5)(3s^6p^-5)

21s¹¹

Power to a Power Rule

100

(x^4)^5

x^20

200

(xy)^6

x^6y^6

300

(4w^5)^2

16w^10

400

4(y^3)^2

4y^6

500

(8w^3y^7)^0

1

600

(k³)² ・ (2k⁴)²

4k¹⁴

Quotient Rule

100

x^7/x^3

x^4

200

(2x^6)/(x^5)

2x

300

(8x^10)/(4x^3)

2x^7

400

u^2/u^9

1/(u^7)

500

(m)/(m^8)

1/(m^7)

600

((a^6b^10)/(3a^2c^8))((a^5b^3)/(a^4c^5))

(a^5b^13)/(3c^13)

Negative Exponent Rule

100

x^-5

1/(x^5)

200

4x^-9

4/(x^9)

300

(5y^3)/(x^-2)

5x²y³

400

(3x^-8)(6x^4)

18/(x^4)

500

(v^5)^-8

1/(v^40)

600

(3a^5b^-4)^3/(a^-4b^-6)^-1

(27a^11)/b^18

Mixed

100

-3x³ (4x^-6)(-x^-2)

12/x⁵

200

⁷(3x²y)(x^-2y²)(10xy⁴)

30xy⁷

300

(12x^7)/(4x^5)

3x²

400

(9x^0y^-6)/(z^-2)

9z^2/(y^6)

500

((2x^2)^4(x^3y^2)(2yx^0))^2

1024x^22y^6

600

((5a^-2b^-2)/(2abc))^-1

(2a^3b^3c)/(5)