Exponent Rules - 8th

Product Rule

100

5² · 5⁴

5²⁺⁴ = 5⁶

200

2² · 2⁸

2²⁺⁸ = 2¹⁰

300

x³ · x⁵

x³⁺⁵ = x⁸

400

x⁰ · x⁶

x⁰⁺⁶ = x⁶

500

x^-2 · x⁵

x^-2+5 = x³

Quotient Rule

100

5^6/5^3

5^6-3 = 5³

200

12^10/12^8

12^10-8 = 12²

300

x^100/x^99

x^100-99 = x¹ or x

400

x^7/x

x^7-1 = x⁶

500

x^2/x^0

x^2-0 = x²

Power of a Product

100

(3² · 5⁴)²

(3^2·2) · (5^4·2) = 3^{4 ·} 5⁸

200

(1⁵ · 9³)³

(1^5·3) · (9^3·3) = 1¹⁵ · 9⁹

300

(x¹⁴ · y⁷)²

(x^14·2) · (y^7·2) = x²⁸y¹⁴

400

(x^-2y^-5)^-2

(x^-2·-2)(y^-5·-2) = x⁴y¹⁰

500

(x¹²y¹⁸)⁰

x^12·0y^18·0 = x⁰y⁰ = 1 · 1 = 1

Power of a quotient

100

(2^2/4^5)^3

2^(2·3)/4^(5·3) = 2^6/4^15

200

(1^2/7^7)^4

1^(2·4)/7^(7·4) = 1^8/7^28

300

((x^5y^6)/z^3)^2

(x^(5·2)y^(6·2))/z^(3·2) = (x^10y^12)/z^6

400

((x^4y^9)/(z^7v^6))^3

(x^(4·3)y^(9·3))/(z^(7·3)v^(6·3)) = (x^12y^27)/(z^21v^18

500

((x^4y^6)/z)^1

(x^(4·1)y^(6·1))/z^(1·1) = (x^4y^6)/z

Zero & Negative Exponents

100

x^-4

1/x^4

200

1/x^-8

x⁸

300

y⁰

1

400

x^-6/(y^-5x^-2

(y^5x^2)/x^6 = y^5x^(2-6) = y^5x^-4 = y^5/x^4

500

(z^-4y^-6)/(z^-4y^-5)

(z^4y^5)/(z^4y^6) = z^(4-4)y^(5-6) = z^0y^-1 = 1/y^1 = 1/y