Exponent Rules

Combining Like Terms

100

3xy+4xy

7xy

200

5a^3b^2-2a^3b^2

3a^3b^2

300

3x^2y+5x^2y^3+2x^2y

5x^2y+5x^2y^3

400

7m^2n^3+5m^3n^3+9m^2n^3

16m^2n^3+5m^3n^3

500

4a³b²c + 2ab²c + 5a³b²c - ab²c

9a^3b^2c+ab^2c

Product Rule

100

x² · x³

x^5

200

a⁴ · a²

a^6

300

5x² · 3x⁴

15x^6

400

(2a³b) · (3a²b³)

6a^5b^4

500

(4x³y²z) · (3x²y³z⁴)

12x^5y^5z^5

Quotient Rule

100

frac{x^5}{x^2}

x^3

200

frac{a^7}{a^3}

a^4

300

frac{3x^6}{x^2}

3x^4

400

frac{6a^5b^2}{2a^2b^3}

frac{3a^3}{b}

500

frac{2x^7y^4}{8x^3y^2}

frac{1}{4}x^4y^2

Power Rule

100

(x²)³

x^6

200

(3a³)^4

81a^12

300

(2x^2y^4)^3

8x^6y^12

400

(2a⁴b²c)²

 

4a^8b^4c^2

500

(-2x³y)^-4

frac{1}{16x^12y^4}

Negative/Zero Exponents

100

x^-2

frac{1}{x^2}

200

2a^3b^-5

frac{2a^3}{b^5}

300

5x^0

5

400

3x^-5y^3z^-1

frac{3y^3}{x^5z}

500

frac{1}{3a^-2b^3}

frac{a^2}{3b^3}

Anything Goes

100

(2x² · x³) + 3x²

2x^5+3x^2

200

frac{a^5}{a^2}*a^3

a^6

300

(5x²)³ · x⁻⁴

125x^2

400

(4x² · 2x⁻³) - x²

frac{8}{x}-x^2

500

frac{(3x^2)^3}{x^4}*x^-5

frac{27}{x^3}