Rational Exponents and Radical Function Review

nth roots/ rational exponents

100

8^2/3

What is 4?

200

81^-3/2

What is 1/729?

300

Rewrite the expression using rational exponent notation: X^7/6

What is the 6th root of x⁷?

400

64^-2/3

What is 1/16?

500

Solve for X: 

X³ + 40 = 25

What is the cube root of -15

Properties of exponents

100

5^{1/2 .} 5^3/2

What is 25?

200

square root of 5 X square root of 20

What is 10?

300

square root of 3 divided by square root of 75

What is 1/5?

400

X^{1/4 .} X^1/3 

What is X^7/12

500

Simplify square root of 49x⁵

What is 7x² square root of x?

Function operations

100

Let f(x)= -3x^1/3 + 4x^1/2  and g(x) = 5x^1/3 + 4x^1/2

^{f(x) + g(x)}

What is 2x^1/3 + 8x^{1/2 ?}

200

Let f(x) = 4x^2/3 and g(x) = 5x^1/2

g(x) ^. g(x) =

What is 25x

300

Let f(x) = 4x^2/3 and g(x) = 5x^1/2

f(x) / g(x) =

What is 4x^1/6 / 5

400

Let f(x) = 4x^2/3 and g(x) = 5x^1/2

g(x) / f(x) =

What is 5 / 4x^1/6 ?

500

Let f(x) = 5x³ + 4x² - x +10

Find f(-4)

What is -242

Function composition

100

Let f(x) = 2x + 3 and h(x) = (x + 5) / 2 .

f(h(x))

What is x + 8?

200

Let f(x) = 3x - 8 and g(x) = 2x²

Find g(f(5))

What is 98?

300

Let f(x) = 2x^-1  and g(x) = 2x + 7

find f(g(x))

What is 2 / (2x+7) ?

400

Let f(x) = 2x^-1  and g(x) = 2x + 7

find g(f(x))

What is (4/x) + 7

500

Let f(x) = 7x² and g(x) = 3x^-2

Find g(f(x))

What is 3/ (49x⁴)?

Inverse functions

100

Find an equation for the inverse relation.

y = 2x + 1

What is 1/2 x - 1/2 ?

200

Find an equation for the inverse relation.

y = -2/3x + 2

What is -3/2x +3 ?

300

f(x) = 32x⁵

find the inverse function

What is 5th root of x / 2 ?

400

f(x) = 2x³ + 1

find the inverse function

What is cube root of (x-1) / 2 ?

500

f(x) = x⁴ - 9

find the f ^-1

What is 4th root of (x+9)