Unit 5: Radicals and Rational Exponents and Functions

Radicals and Rational Exponents

100

Use the properties of rational exponents to simplify the expression. 

(14³)^1/2

14^3/2

200

Use the properties of rational exponents to simplify the expression.

(9^-3/5 x 9^1/5)^-1

9^2/5 or 3^4/5

300

Use the properties of rational exponents to simplify the expression.

25^5/9 x 25^7/9 / 5^4/3

5^4/3

400

Use the properties of radicals to simplify the expression.

√7/√700

1/10

500

Simplify the expression.

13 ³√3 - ³√375

8 ³√3

Radical and Rational Equations

100

Solve the equation. Make sure to check for extraneous solutions!

9 = √p+7

p = 74

Check

9 = √74+7

9 = √81

9 = 9 

200

Solve the equation. Remember to check for extraneous solutions!

√-6 - v = √v + 10

v = -8 

Check

√-6 - (-8) = √-8 + 10

√-6 + 8 = √2

√2 = √2

300

Solve the equation. Check solution(s)

-2 + 4(3x - 36)^3/2 = 106

x = 15

400

Solve the equation. Check solution(s)

1276 = -4 + 5(8 - 4r)^4/3 

r = -14 and r = 18

500

Solve the equation. Check your answer!

√(4x+7) + √(6x+6) = √(20x+26)

x = 1/2

Radical Inequalities

100

Solve the inequality. Check your solution!

4√(x) + 3 ≤ 23

0 ≤ x ≤ 25 

[0,25] 

200

Solve the inequality. Check your solution!

√(x+10) ≥ 6

x ≥ 26 

[26,∞) 

300

Solve the inequality. Check your solution!

√(2x+6) - 3 ≤ 1

-3 ≤ x ≤ 5 

[-3,5]

400

Solve the inequality. Check your solution!

-3√(x+2) < 15

x ≥ -2 

[-2,∞)

500

Solve the inequality. Check your solution!

5 - √(20x +4) ≥ -3

-1/5 ≤ x ≤ 3

[-1/5,3]

Function Operations

100

Perform the indicated operation to write the new function rule.

g(t) = −t + 3

h(t) = 3t − 4

Find (g ⋅ h)(t)

−3t² + 13t − 12

200

Perform the indicated operation to write the new function rule.

h(t) = 2t + 1

g(t) = 2t + 2

Find (h − g)(t)

-1

300

Perform the indicated operation to write the new function rule.

g(n) = 3n + 2 

f (n) = 2n² + 5 

Find g( f (2))

41 

400

Perform the indicated operation to write the new function rule.

h(a) = 3a 

g(a) = −a³ − 3 

Find (h/g) (a)

3a / (−a³ − 3)

500

Perform the indicated operation to write the new function rule.

h(x) = x² − 2 

g(x) = 4x + 1 

Find (h ∘ g)(x)

16x² + 8x − 1

Function Composition

100

Given f (x) = x - 1 and g(x) = 5x+ 2, find:

f (g(2))

11