Properties of Exponents

Additive Law

100

(2^3)(2^5)

2^8

200

v^8*v^3

v^11

300

(1/2)^3*(1/2)^4

(1/2)^7

400

x^-5*x

1/(x^4)

500

-6m^5*12m^7

-72m^12

Power of a Power

100

(2^3)^2

2^6

200

(10^4)^4

10^16

300

((2/3)^5)^3

(2/3)^15

400

(x^5)^-3

1/(x^15)

500

(5x^4)^3

125x^12

Quotients of Powers

100

2^8/(2^3)

2⁵

200

x^6/(x^5

x

300

5^2/(5^5)

1/(5^3)

400

(12p^5)/(6p)

2p^4

500

(10x^2y^7)/(2x^4y^3)

(5y^4)/(x^2)

Negative and Zero Exponents

100

2^0

1

200

2^-19

1/2^(19)

300

(6^-2)^0

1

400

(x^3)^-2

1/x^6

500

(3/5)^-7

(5/3)^7

Fractional Exponents

100

3^(1/2

sqrt(3)

200

x^(1/3)

root(3)(x)

300

2^(3/5)

root(5)(2^3) or (root(5)(2))^3

400

x^(5/9)

root(9)(x^5) or (root(9)(x))^5

500

(1/2)^(3/2)

root(2)((1/2)^3) or (root(2)(1/2))^3