Simplifying Radical Form
Conversion Between Rational Exponent Form and Radical Form
Simplest Form
Multiplying & Dividing
Properties
100

Simplify

sqrt(36)

 using rational exponents.

6

100

Convert

y^3.5

 to radical form.

sqrt(y^7)

100

Simplify.

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

5

100

root(3)(6)*sqrt(2)

Cannot multiply; Different indexes

100

am x an = am+n

Product of Powers

200

Simplify

root(4)(16)

 using rational exponents.

2

200

Convert

(root(5)(b))^3

 to exponential form.

b^(3/5)

200

Simplify.

25^(-3/2)

1/125

200

sqrt(72x^3y^2)*sqrt(10xy^3)

12x^2y^2sqrt(5y)

200

(am)n = amn

Power of a Power

300

Simplify

root(3)(-27)

 using rational exponents.

-3

300

Convert to exponential form.

sqrt(a^5)

a^(5/2)

300

Simplify.

4^(-3.5)

1/128

300

(sqrt(18x^5))/(sqrt(2x^3))

3x

300

a0=1

Zero Exponent

400

Simplify

root(3)(3^2)

 using rational exponents.

3^(2/3)

400

Convert to exponential form.

root(4)(x^3)

x^(3/4)

400

Simplify.

4/(root(3)(1331))

4/11

400

sqrt(45x^5y^4)*sqrt(35xy^4)

15xy^4sqrt(7x^5)

400

(ab)m = ambm

Power of a Product aka distribute

500

Simplify

root(3)(-16^2)

 using rational exponents.

-4(2^(2/3))

500

Convert to radical form.

w^(-5/8)

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

500

Simplify.

(root(3)(x))/(root(6)(x^5))

(sqrt(x))/x

500

(root(3)(162y^5))/(root(3)(3y^2))

3yroot(3)(2)

500

a-m = 1/am

Negative Exponent