Exponent Laws

Multiplying Powers

100

(x³)(x⁴)

x⁷

200

(3³)(3²)(3)

3⁶  or  729

300

(-12x⁷y²)(8x²y⁶)

-96x⁹y⁸

400

(8x⁴y⁶)(-5x¹⁰y³)

-40x¹⁴y⁹

500

(7x¹⁰y⁹z⁷)(-2x⁸yz)

-14x¹⁸y¹⁰z⁸

Dividing Powers

100

(x^12)/(x^7)

x⁵

200

(5^5)/(5^3)

5²  or 25

300

(7x^12y^4z)/(14x^7y^2)

(x^5y^2z)/2

400

(18x^8y^3z)/(4x^3y^8z^3)

(9x^5)/(2y^5z^2)

500

(3x^2yz^5)/(15x^7y^3z^4)

(z)/(5x^5y^2)

Power to a Power

100

(x⁶)³

x¹⁸

200

(2⁵)²

2¹⁰  or 1,024 

300

(-8²)³

-8⁶  or  -262,144

400

(2x³y⁵)³

8x⁹y¹⁵

500

(-3x²y⁴z⁷)³

-27x⁶y¹²z²¹

Name that Rule

100

a^m x aⁿ = a^m+n

Product Rule

200

(a^m)ⁿ = a^mn

Power Rule

300

a^m/aⁿ = a^m-n

Quotient Rule

400

(3x²)(2x⁴)

Product Rule

500

(x⁷y⁴)⁵

Power Rule

Mixed Goodies

100

(x⁴)² (x³)

x¹¹

200

(2⁴)(2⁷)³

2^25

300

((3x^3)^2)/(6x)

(3x^5)/(2)

400

(-4x⁸y)(2xy)³

-32x^11y^4

500

(-2x¹²)³(-8x²)²(x⁶)⁷

-512x⁸²