Radicals Review

Radically Simple

100

Simplify:

root(3)(216x^5)

6x^(5/3)

200

Simplify and write in rational exponent form:

sqrt(4)*sqrt(4^3)

16 or 4^2

300

Simplify and write in terms of rational exponents:

root(3)(27x^7) * sqrt(16x^3)

12x^(23/6)

400

Simplify and write in terms of rational exponents:

root(4)((2x^3)/(32x^9)

1/(2x^(6/4))

500

Simplify and write with rational exponents:

sqrt(18x^3y^4)*sqrt(8x^2y^5)

12x^(5/2)y^(9/2)

Converting Between Forms

100

Convert to rational exponent form:

root(3)(x^2)

x^(2/3)

200

Convert to radical form:

y^(1/5)

root(5)(y)

300

Convert to radical form:

(2x^2)^(4/3)

(root(3)(16x^8))

400

Convert to rational exponent form:

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

(3x)^(-2/3)

500

Convert to radical form:

(16x^4)^(-1/4)

1/(2x)

Simplifying Exponents

100

Simplify:

x^4/x^2

x^2

200

Simplify:

(x^5*x^3y^3)^3

x^24y^9

300

Simplify:

((-m)/(-m^2*-m^0))^4

1/m^4

400

Simplify:

(-x^4y^4)/(-y^4*(-y^-5)^4)

x^4y^20

500

Simplify:

((pq^-2*p^4q^(-1/2))/(p^(1/3)q^(1/2)r^(-3/2)*p^(3/2)q^(3/4)r^(1/2)))^2

(r^2p^(19/3))/q^(15/2)

Solving Equations

100

Solve for x:

sqrt(x)=49

x=2401

200

Solve for v:

v=sqrt(-10+11v)

v= 1, 10

300

Solve for r:

2048 = 2r^(5/3)

r=64

400

Solve for n:

1/128 = (4n)^(-7/5)

n=8

500

Solve for a:

4root(3)(-14-3a) -9 = 7

a=-26

I can do this?

100

Simplify:

sqrt(64)

8

200

Simplify and write in terms of rational exponents:

root(4)(sqrt(p))

p^(1/8)

300

Simplify and write in terms of rational exponents.

sqrt(b) * sqrt(sqrt(b))

b^(3/4)

400

Simplify and write in terms of rational exponents:

(sqrt(v))/(2(sqrt(v))^-3

v^2/2

500

Simplify and write in terms of rational exponents:

(sqrtp^-1p^0)/((root(3)(root(3)(p^5)))^-4

p^(31/18)