exponential and radical review

Simplifying Radicals

100

Simplify the following radical expression

sqrt(98)

7sqrt2

200

Simplify the following radical expression

5sqrt(112)

20sqrt7

300

Simplify the following radical expression

sqrt(192xy^11z^6)

8y^5z^3sqrt(3xy)

400

Simplify the following radical expression

4root3(125x^9y^7)

20x^3y^2root3(y)

500

Simplify the following radical expression

root5(288x^3y^7)

2yroot5(9x^3y^2)

Radical Form to Exponential Form

100

Convert the following expression from Radical Form to Exponential Form

root5(n^4)

n^(4/5)

200

Convert the following expression from Radical Form to Exponential Form

root3(-27m^2n^6)

-3m^(2/3)n^2

300

Convert the following expression from Radical Form to Exponential Form

root4((5ab)^3)

5^(3/4)a^(3/4)b^(3/4)

OR

125^(1/4)a^(3/4)b^(3/4)

400

Convert the following expression from Radical Form to Exponential Form

root4(5ab^3)

5^(1/4)a^(1/4)b^(3/4)

Exponential Form to Radical Form

100

Convert the following expression from Rational Exponents to Simplest Radical Form

x^(2/5)

root(5)(x^2)

(root(5)x)^2

200

Convert the following expression from Rational Exponents to Simplest Radical Form

7x^(2/3)

7root(3)x^2

7(root(3)x)^2

300

Convert the following expression from Rational Exponents to Simplest Radical Form

x^(17/2)

x^8sqrtx

400

Convert the following expression from Rational Exponents to Simplest Radical Form

(4x)^(5/2)

2x^2sqrtx

500

Convert the following expression from Rational Exponents to Simplest Radical Form

(12^3x)^(1/2)

6x^2sqrt6x

Solving Radical Equations

100

Solve the given radical equation

(x-2)^(1/2)=5

x=27

200

Solve the given radical equation

2x^(3/4)=16

x=16

300

Solve the given radical equation

root3(13x-1)-4=0

x=5

400

Solve the given radical equation

3x^(4/3)+5=53

x=8 and x =-8

500

Solve the given radical equation

sqrt(7x+43)=x+5

x = 3.   x = -6 is extraneous