Unit 7.1-7.3

Rational Exponent Properties

100

3a^7/3 - 7a^7/3 + 3b^7/3

-4a^7/3 + 3b^7/3

200

3b^-1/2 x 4ab²

12ab^3/2

300

m^5/4 x (m²)^7/4

m^19/4

400

(a^4/2)² x b^-1a^1/3

(a^13/3)/b

500

(a⁰b^-1)/((a^-2b)^5/3)

(a^10/3)/(b^8/3)

Harder Rational Exponent Properties

100

(b² x a^4/3b^3/2)^3/2

a²b^21/4

200

sqrt(36n⁸)

6n⁴

300

uv⁰ x u⁰ x (2u⁴v^2/3)⁰

u

400

eighth root((2x²)³(2x²)⁵)

2x²

500

cube root( fourth root(a)) x (sqrt( cube root(a))

a^1/4

Solve for Variables

100

v⁴ - 6 = 619

v = +/- 5 or v = 5, -5

200

(3x-6)² = 0

x = 2

300

-2 + sqrt(b) = 5

b = 49

400

-35 = 10 - 5p^1/2

81 = p

500

-4(a+14)^3/2 = -256

a = 2

Function Operations

100

f(x) = 32x² - 4x - 4

g(x) = 13 + 2x

What is g(x) + f(x)?

32x² - 2x + 9

200

f(x) = 2x^1/5 - 3x^5/3

g(x) = x² + 12x - 3

What is f(x) - g(x)?

x² - 3x^5/3 + 12x + 2x^1/5 - 3

300

f(x) = 2x - 4

g(x) = .5x + 8x²

What is (f(x))(g(x))?

16x³ - 31x² - 2x

400

f(x) = (x+5)²

g(x) = -3x² + 4x³ + 2x

What is f(x) - g(x)?

-4x³ + 4x² + 8x + 25

500

f(x) = 4x² - 12x

g(x) = 3x+1

h(x) = 1/(2x)

What is (f(x))/(h(x)) + g(x)?

5x - 5

Domain

100

Check Canva

2<x<8 or [2, 8)

200

f(x) = 3x - 10

-infinity < x < infinity or (-oo, oo)

300

f(x) = 5x⁵ + 2x^1/2

0 < x < infinity or [0,oo)

400

f(x) = (12-2x)/(12x² + 2x)

0 < x < infinity or (0, oo)

500

f(x) = ((3x) - 4x⁵ + ((3x^1/2)/(4x²-2))) - 12x³

0 < x < infinity or (0, oo)