Algebra 2: Radical and Rational Exponents

Simplifying Radical Form

100

Simplify

sqrt(36)

 using rational exponents.

6

200

Simplify

root(4)(16)

 using rational exponents.

2

300

Simplify

root(3)(-27)

 using rational exponents.

-3

400

Simplify

root(3)(8^2)

 using rational exponents.

4

500

Simplify Completely

27^(-2/3)

1/9

Conversion Between Rational Exponent Form and Radical Form

100

Convert

y^(7/2)

 to radical form.

sqrt(y^7)

200

Convert

(root(5)(b))^3

 to exponential form.

b^(3/5)

300

Convert to exponential form.

sqrt(a^5)

a^(5/2)

400

Convert to exponential form.

root(4)(x^3)

x^(3/4)

500

Rewrite using radicals and no negative powers

w^(-5/8)

1/(root(8)(w^5))

Simplest Form

100

Simplify.

5^(1/2)*5^(1/2)

5

200

Simplify.

25^(-3/2)

1/125

300

Simplify.

4^(7/2)

128

400

Simplify Completely

16^(1/2)8^(1/3)

8

500

Simplify Completely

8^(1/2)8^(3/2)

64