Properties of Rational Exponents

Write in radical form (no variables)

100

Write 10^1/2 in radical form.

Square root of 10

200

Write 8^1/3 in radical form.

Cubic root of 8

300

Write 4^4/3 in radical form.

(Cubic root of 4)⁴

400

Write 7^4/3 in radical form.

(Cubic root of 7)⁴

500

Write 2^1/6 in radical form.

6th root of 2

Write in Exponential Form (no variables)

100

√8

8^1/2

200

³ √11

11^1/3

300

⁶ √2

2^1/6

400

(⁴ √5)⁵

5^5/4

500

⁶ √10

10^1/6

Write in Radical Form (with variables)

100

3y^1/3

³ √3y

200

5^-1/2

1/( √5)

300

(5x)^-1/2

1/( √5x)

400

a^6/5

(⁵ √6)⁶

500

m^-1/2

1/( √m)

Write in Exponential form (with variables)

100

(³ √y)

y^1/3

200

( √2y)

2y^1/2

400

 √6p

6p^1/2

500

1/(( √3k)⁵)

3k^-5/2

Simplify Rational Exponents

100

(x⁶)^1/2

x³

200

(64n)^-1/2

1/( √64n)

300

36^3/2

216

400

(9n⁴)^1/2

3n²

500

(81m⁶)^1/2

9m³