Exponent Laws

Combinations

100

(x^2*x^5)^3

x^21

200

(g^6/g)^5

g^25

300

Write with positive exponents. (h^-3)^2 

1/h^6

400

(27a^5b^7)/(3ab)

9a^4b^6

500

((8m^14n^9)/(6m^9n^3))^2

(16m^10n^12)/9

Multiplication

100

x^2*x^7

x^9

200

x^6*x

x^7

300

q^8*q^-3

q^5

400

x^6y^3*x^2y^11

x^8y^14

500

3xy^6*5xy^-2

15x^2y^4

Power of a Power

100

(x^3)^4

x^12

200

(x^-3)^2

x^-6

300

(x^3y^7)^6

x^18y^42

400

(x^(1/2))^(1/2)

x^(1/4)

500

(2x^3)^3

8x^9

Division

100

x^6/x^2

x^4

200

y^5/y^-2

y^7

300

t^(3/4)/t^(1/4)

y^(1/2)    OR    y^(2/4)

400

(u^9v^6)/(vu^4)

u^5v^5

500

(15s^13t^8)/(5s^8t^5)

3s^5t^3

Negative Exponents

100

Write with positive exponents.  x^-4 

1/x^4

200

Write with positive exponents. 1/r^-2 

r^2

300

Write with positive exponents. 

2x^-6y^3

(2y^3)/x^6

400

Write with positive exponents. 

(3x^-10)/y^-3

(3y^3)/x^10

500

Write with positive exponents. 

(5x^4)/(y^-3z^4)

(5x^4y^3)/z^4