Rational and Radical Exponents

Change to Exponent Form

100

Write the radical in exponential form.

sqrt(19)

19^(1/2)

200

Write the radical in exponential form.

root(4)(63)

 

63^(1/4)

300

Write the radical in exponential form.

root(3)(y^2)

y^(2/3)

400

Write the radical in exponential form.

root(4)(x^4)

x

500

Write the radical in exponential form.

root(3)(x^6y^8)

x^2y^(8/3)

Change to Radical Form

100

Write the rational expression in radical form.

8^(1/5)

 

root(5)(8)

200

Write the rational expression in radical form.

a^(3/4)

 

root(4)(a^3)

300

Write the rational expression in radical form.

4^(2/7)

root(7)(16)

400

Write the rational expression in radical form.

(x^3)^(3/2)

sqrt(x^9)

500

Write the rational expression in radical form.

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

root(5)(a^3)

Simplify

100

Simplify.  

32^(1/5)

2

200

Simplify.  

x^(7/8)/x^(5/8)

x^(1/4)

300

Simplify.

b^(4/9)*b^(5/9)

b

400

Simplify.

(y^(1/4))^(3/5)

y^(3/20)

500

Simplify.

(64x^3)^(2/3)

16x^2

Solve Radical Equations

100

Solve.

6+sqrt(3x+1)=11

x = 8

200

Solve.

sqrt(x-3)= 3

x = 12

300

Solve.

3sqrt(x-10)= 18

x = 46

400

Solve.

2+sqrt(3y-5)=10

y = 23

500

Solve.

7-5sqrt(b-6)= 32

b = 31

Solve with Rational Exponent

100

Solve.

(5n-6)^(1/3)+3=4

n = 7/5

200

Solve.

(6q+1)^(1/4)+2=5

q = 40/3

300

Solve.

(3y-2)^(1/5)+5=6

y = 1

400

Solve.

(5x+10)^(1/3)-5=0

x = 23

500

Solve.

1/4(32b)^(1/3)=1

b = 2