Algebra 2 Rational Expressions Review

Rewrite in radical form.

100

28^1/2

√28 = √4 * √7 = 2√7

200

2^4/3

³√2⁴ = ³√16 = ³√8 * ³√2 = 2³√2

300

(256x)^1/4

⁴√256x = ⁴√256 * ⁴√x = 4 ⁴√x

400

(mn)^7/2

√(mn)⁷ = √(mn)⁶ * √(mn) = m³n³ √mn

500

(-2a)^4/3

³√(-2a)⁴ = ³√16a⁴ = ³√8a³ * ³√2a = 2a ³√2a

Rewrite in exponential form.

100

⁴√10³

10^3/4

200

√3ab

(3ab)^1/2 = 3^1/2 a^1/2 b^1/2 

300

(³√2w)⁵

(2x)^5/3 = 2^5/3 * w^5/3 = 32^1/3 w^5/3

400

⁴√18x⁶y²

(18x⁶y²)^1/4 = 18^1/4 x^3/2 y^1/2

500

⁸√9x²y¹²

(9x²y¹²)^1/8 = 9^1/8 x^1/4 y^3/2

Simplify in simplest radical form.

100

45^-3/2 * 45²

45^1/2 = √45 = √9 * √5 = 3√5

200

(28^3/5)^5/6

28^15/30 = 28^1/2 = √28 = √4 * √7 = 2√7

300

³√24⁴ / 24

24^4/3 / 24 = 24^1/3 = ³√24 = ³√8 * ³√3 = 2³√3

400

⁴√p * √p³

p^1/4 * p^3/2 = p^7/4 = ⁴√p⁷ = ⁴√p⁴ * ⁴√p³ = p ⁴√p³ 

500

⁴√a²b¹⁴

a^2/4 b^14/4 = a^1/2 b^7/2 = √ab⁷ = √b⁶ √ab = b³√ab

Simplify in simplest radical form.

100

m / ⁴√m 

m / m^1/4 = m^3/4 = ⁴√m³

200

16 / ⁴√16³

16 / 16^3/4 = 16^1-3/4 = 16^1/4 = ⁴√16 = 2

300

(-64)^-1/3

1 / (-64)^1/3 = 1 / ³√-64 = 1 / -4

400

2(48/3)^-1/4

2(16)^-1/4 = 2(1/16)^1/4 = 2 ⁴√(1/16) = 2(1/2) = 1

500

⁴√36w⁶

(36w⁶)^1/4 = (6²w⁶)^1/4 = 6^1/2 * w^3/2 

= √6w³ = √w² √6w = w√6w