Exponents

product rule same base

100

2^2 x 2^4

2⁽²⁺⁴⁾   

2⁶

200

3⁸ x 3⁴

3⁽⁸⁺⁴⁾ 

3¹²

300

9^-4 x 9^-8 

9^{(-4 + -8)} 

9^-12

(1/9^12)

400

10^-2 x 10⁵ 

10^{(-2 + 5)}

10³

500

4⁰x4^-4

4^(0+(-4))

4^-4

(1/4^4)

600

8^-4 x 8⁰

8^(-4+0)

8-⁴

1/(8^4)

quotient rule same base

100

9³ / 9²

9^(3-2)

9¹

200

2¹⁰ / 2⁸

2^(10-8)

2²

300

3^-4 / 3²

3^(-4-2)

3^-6

1/(3^6)

400

6^-3 / 6²

6^(-3-2)

6^-5

1/(6^5)

500

8^-2 / 8^-4

8^(-2-(-4))   8^(-2+4)

8²

600

9³ / 9^-4

9^(3-(-4))  9⁽³⁺⁴⁾

9⁷

quotient rule different base

100

3⁶ / 1⁶

3⁶

200

9² / 3²

3²

300

18⁴ / 2⁴

9⁴

400

200³⁰ / 10³⁰

20³⁰

500

-4² / 2²

-2²

600

-8⁶ / -2⁶

4⁶

product rule different base

100

9² x 3²

27²

200

4^-4 x 6^-4

24^-4

(1/24^4)

300

12³ x 3³

36³

400

-2⁵ x 3⁵

-6⁵

500

-8-⁶ x 2-⁶

-16-⁶

1/(16^6)

600

-2-⁴ x -6-⁴

12-⁴

1/(12^4)

power rule

100

(3x)²

3²x²

9x²

200

(7x³)⁴

7⁴ x¹²

2401x¹²

300

(2x²y)³

2³x⁶y³

8x⁶y³

400

((3x^2)/(4y^4))^2

(9x^4)/(16y^16)

500

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

(4y^2)/(9x^2)

600

((3y^0)/(y^-2))^2

3y^4

Simplify

100

(x^6)/(x^4)

X²

200

(s^6y^2z^3)/(s^8yz^5)

y/(s^2z^2)

300

(z^6t^2q^4)/(q^7t^3)

(z^6t)/(q^3)

400

(y^-8)/(y^2)

1/y^10

500

z^-4/z^-2

1/z^2

600

(8z^6y^3)^2/(y^7z^3)

(8z^9)/y