Nth Roots and Rational Exponents

Solve for x, (x − 5)⁴ = 256

• x = 9

• x = 1

• x = 1 and x = 9

• x = -1 and x = -9

Find the indicated real n^th root(s) of a. n = 8 , a = 256

• 2

• -2

• ±2

• no real roots

Find the real solution(s) of (x + 3)⁴ = 24.

• x ≈ 2.14

• x ≈ 2.14 or x ≈ -2.14

• x ≈ - 0.79 or x ≈ -5.21

• x ≈ - 0.79

An expression containing a radical with index n is in simplest form when these three conditions are met.

• No radicands have perfect nth powers as factors.

• No radicands contain negative numbers.

• No radicands contain fractions.

• No radicals appear in the numerator of a fraction.

• No radicals appear in the denominator of a fraction.

Write in simplest form. ∛500

• 167 ⅔

• 5 ∛4

• 10 √5

• 3 ∛167

To rationalize a denominator of 2 - √7

• multiply the numerator and denominator by √7

• multiply the denominator by 2 + √7

• multiply the numerator and denominator by 2 - √7

• multiply the numerator and denominator by 2 + √7

• multiply the denominator by √7

Simplify ∛(27d¹²)

• 9d⁴

• 3d⁴

• 3d⁹

• 9d⁹

• y²z¹⁰√xy
• 20yz√xy
• xy²z¹⁰√y
• yz⁶√xy²z²

Rewrite in Radical Form.

• A

• B

• C

• D

Rewrite in radical form.

• A

• B

• C

• D