Exponent Rules

Add/Sub

100

-4xy³ + 10xy³ - 2xy⁴

6xy³ - 2xy⁴

200

2ab⁴c + 5a²b - ab⁴c - 6a²b

ab⁴c - a²b

300

Find the sum of 3gh and -5gh, then subtract 2gh

-4gh

400

Subtract -5p²n from 6p²n

11p²n

500

-6ab - ab + a²b - 4ab - a²b + 5a²b - 2ab + a³b + 4ab

-9ab + 5a²b + a³b

Multiplying/Divide

100

(x²y)(xy⁴)

x³y⁵

200

(-9a⁶b⁵c²)(-ab⁵c¹¹)

9a⁷b¹⁰c¹³

300

4x⁵y³z⁸w¹¹

^{_____________}

2x³y³z⁸w⁷

2x²w⁴

400

(-6r³m¹⁵)(rm²)(-5r²m)

30r⁶m¹⁸

500

-24a¹³b⁴

^___________

32a¹²b

-3/4ab³

Powers

100

(p⁵)⁵

p²⁵

200

(-d⁴e²)⁶

d²⁴e¹²

300

(-5c²d)³

-125c⁶d³

400

(-3x²y⁷z)³

-27x⁶y²¹z³

500

(-1/4 ab⁴)⁶

^{Keep answer in fraction form}

1/4096 a⁶b²⁴

Geometry

100

Find the perimeter of a rectangle which has a length of 8a⁵b and a width of 4a⁵b⁷

16a²b + 8a⁵b⁷

200

Find the area of a rectangle that has a width of 5x²y and a length of 3y³

15x²y⁴

300

Find the area of a triangle that has a base of 6x⁴y² and a height of 5xy⁷

15x⁵y⁹

400

Find the area of a circle with a radius of 2.5a²b⁴

19.625a⁴b⁸

500

Find the area of a trapezoid that has bases that measure 4xy and 8xy and a height of 3x²

18x³y

Mixed

100

(-2a⁴)³ (7a⁵)

-56a¹⁷

200

(3xy²)²(4x⁵y⁸)²

^{_________________}

    72x⁴y²⁰

2x⁸

300

(28n³p⁴)²

________________           + 5n²p⁴

(2np)⁴

54n²p⁴

400

(-5k⁶w⁷)² - (-k³w)³(3k³w¹¹)

28k¹²w¹⁴

500

(2x³)²(3y⁴)³

__________________        - 4x²y⁷

  12x⁴y⁵

5x²y⁷