exponents

Product Rule of Power

100

3^{5  /} 3³

3⁵ /3³   

3^5-3

3²

200

2(x² y⁵) 

2(x² y⁵)

2x² y⁵

2*2x² y⁵

4x²y⁵

300

(x³y⁵z²)(x²y⁷z⁵ )

(x³y⁵z²)(x²y⁷z⁵ )

x⁽³⁺²⁾ y⁽⁵⁺⁷⁾ z⁽²⁺⁵⁾

x⁵y¹²z⁷

400

(x³y⁵z²)(x²y⁷z⁵)

(x³y⁵z²)(x²y⁷z⁵)

x⁽³⁺²⁾y⁽⁵⁺⁷⁾z⁽²⁺⁵⁾

x⁵y¹²z⁷

500

3²* 3⁵*3⁶*3⁷*3¹⁰

3²* 3⁵*3⁶*3⁷*3¹⁰

(3*3*3*3*3)^(2+5+6+7+10)

(9*9*3)^(2+5+6+7+10)

(81*3)^(2+5+6+7+10)

(243)^(2+5+6+7+10)

243³⁰

Quotient Rule of Power

100

x⁵/x²

x⁵/x²

x^(5-2)

x³

200

x²³ * x² / x⁴

x²³ * x² / x⁴

x⁽²³⁺²⁾/ x⁴

x²⁵ / x⁴

x(^25-4)

x²¹

300

x⁴ y²² / x² y²⁰

x⁴ y²² / x² y²⁰

x^(4-2)y^(22-20)

x²  y²

400

x⁴⁵ y² /x⁴⁷ y²

x⁴⁵ y² /x⁴⁷ y²

x^(45-47) y^(2-2)

1/x²

500

x³ y⁵ z²⁵/z¹⁰⁰ y²⁵ x⁴² 

x³ y⁵ z²⁵/z¹⁰⁰ y²⁵ x⁴²

x^(3-100) y^(5-25) z^(25-42)

1 /x⁹⁷  y²⁰ z²³

Negative Exponents

100

4^-2

4^-2

1 / 4²

1/4*4

1/16

200

-4x5y^-2

-4x5y^-2

-4x5/y²

(-4*5)x/y²

-20x/y²

300

-7x⁷y^-2(6²x⁵)

-7x⁷y^-2(6²x⁵)

-7x⁷(6*6) x⁵/y²

(-7*36)x⁷⁺⁵/y²

252x¹²/y²

400

(x²/y)^-3

(x²/y)^-3

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

x^-6 y^-3

1/x⁶ y³

500

(-2x²y^-4)(5*2x^-3)

(-2x²y^-4)(5*2x^-3)

(-2*10)x²/y⁴x³

-20x^(3-2)/y⁴

-20/xy⁴

Miscellaneous

100

5⁰*5⁴

5⁰*5⁴

1*(5*5*5*5)

1*(625)

625

200

(5x²)⁴

(5x²)⁴

5⁴x⁸

(5*5*5*5)x⁸

625x⁸

300

(5x³)* (6^-2*5x)

(5) (x³)(6^-2)* 5x

(5*5)x⁽³⁺¹⁾/6²

25x⁴/(6*6)

25x⁴/36

400

(5y^-3)^-3 (4x²* y⁵)

(5y^-3)^-3 (4x²* y⁵)

(5^-3)(y⁹) (4x²* y⁵)

(y⁹) (4x²* y⁵)/(5^-3)

y⁽⁵⁺⁹⁾(4x²)/(125)

4x²y¹⁴/125

500

(5x³)(xy^-5)(6x²y⁵x^-3)

(5x³)(xy^-5)(6x²y⁵x^-3)

(6*5x^(3+1+2)y⁵/y⁵x³

(6*5)x⁶y^(5-5)/x³

30x6^-3

30x³

Properties of Exponents

100

4v³*vu²

4v³*vu²

4v⁽³⁺¹⁾u²

4v⁴u²

200

4v³*7v^-3

4v³*7v^-3

7*4v³/v³

28v^(3-3)

28

300

2x³y^-3*2x^-1y³

2x³y^-3*2x^-1y³

(2*2)x³y³/y³x

4x^(3-1)y^(3-3)

4x²

400

4x²y³x^-3/5x⁴x^-5y²

4x²y³x^-3/5x⁴x^-5y²

4x²x⁵y³/5x⁴y²x³

4x(²⁺⁵⁾y³/5x⁴⁺³y²

4x⁷y³/5x⁷y²

4x^(7-7)y^(3-2)/5

4y/5

500

(6x²y⁵)⁵/5²x⁴y³

(6x²y⁵)⁵/5²x⁴y³

(6⁵x¹⁰y²⁵)/25x⁴y³

7776x^10-4y^25-3/25

7775x⁶y²⁶

311.04x⁶y²²