exponents

product rule

100

a^3 x a^6

a^9

200

3a^3 x 2a^6

5a^9

300

(-5a^5b)^4 (8a^4b)

-40a^9b^2

power rule

100

(x^5)^6

x^30

200

(x^5)^3 x x^2

x^17

300

(2x^3)^4 x 5x^2

21x^15

500

(9x^5)^3/1x^-2

792x^17

quotient rule

100

x^9/x^7

x^2

200

30x^7/22x^5

2x^2+3x-2x-3-x^2-3x/(x-1)^2

negative exponent

100

3x^-2

3/x^2

200

x^-1

1/x

300

x^-3​​​​

1/x³

400

(x^-2b³)⁴

y¹²/x⁸

500

(a-⁶b¹⁰c^-4)/(a⁶b^-3c³)

(b¹³)/(a¹²c⁷)

zero exponent rule

100

5^0

1

200

x^0+7

8

300

(3^0+4^0)x2

4

400

(9^0+2^0)/7^0

2

500

(x^0y^0+4z^0)/(2y^3)

1/2+2/y^3