Exponents and Radical Expressions

Combining Like Terms

100

sqrt(5a) + 3 sqrt(5a)

4 sqrt(5a)

200

6 sqrt(5) - 12 sqrt(5) + sqrt(15)

-6 sqrt(5) + sqrt(15) 

300

8 sqrt(3) + 5 sqrt(3) - 6 sqrt(2) + sqrt(2)

13 sqrt(3) - 5 sqrt(2)

400

root(3)(125) + sqrt(81) - root(3)(6)

14 - root(3)(6)

500

sqrt(16) + sqrt(8) - root(3)(1000) - root(3)(2000)

-6 + 2 sqrt(2) - 10 root(3)(2)

Positive ExponentsSimplify

100

(x^25 y^2 z^3)/(x^(-11) y^15 z^-3)

(x^36 z^6)/(y^13)

200

((b^12 d^-3)/(a^3 c^6))^(1/3)

(b^4)/(a c^2 d)

300

((5^-1 x^4)/(3y^5z^-1))^-2

(3^2 5^2y^10)/(x^8z^2) or (225y^10)/(x^8z^2)

400

(x^3y^(1/2))^3/(3x)^0 . (2x^5)^-1/(5xy^(1/2))^2

(x^2 y^(1/2))/(50)

500

(5a^8b^0)^(1/2) . ((a^4b^5)/(10a^11(b^6)^2))

(5^(1/2))/(10a^3b^7)

Rational ExponentsSimplify

100

Write in Radical Form

sqrt(18a^20y^4)

3a^10y^2 sqrt(2)

200

sqrt(15x^100y^5)

x^50y^2 sqrt(15y)

300

root(3)(x^19y^14z^12)

x^6y^4z^4 root(3)(xy^3)

400

root(3)(48x^18y^7

2x^6y^2 root(3)(6y)

500

root(3)(54x^22y^20)

3x^7y^2 root(3)2xy^2)

Solve for a

100

7^8 = (7^a)^(1/2)

a = 16

200

4^(3/5) = 2^a

a = 6/5

300

1/7 = 7^(a/9)

a = -9

400

1/9^3 = (9^2)^a

a = - 3/2

500

10^-2 = a/100

a = 1

Solve for all Possible SolutionsOne, Two, or No Real Solutions

100

x^2 + 6 = 18

x = +-2 sqrt3

200

p^2 + 2 = 1

no real solution

300

x^2 - 75 = 0

x = +-5sqrt3

400

sqrt(3x - 2) = 0

x = 2/3

500

sqrt(1/2x + 1) = 5

x = 48