Rational and Radical Exponents

Change to Rational form

100

Write the radical in exponential form.

sqrt(19)

19^(1/2)

200

Write the radical in exponential form.

root(4)(63)

 

63^(1/4)

300

Write the radical in exponential form.

root(3)(5xy^2)

5^(1/3)x^(1/3)y^(2/3)

400

Write the radical in exponential form.

root(4)(625x^4)

5x

500

Write the radical in exponential form.

root(3)(27x^6y^8z)

3x^2y^(8/3)z^(1/3)

Change to Radical Form

100

Write the rational expression in radical form.

8^(1/5)

 

root(5)(8)

200

Write the rational expression in radical form.

a^(3/4)

 

root(4)(a^3)

300

Write the rational expression in radical form.

4^(2/7)

root(7)(16)

400

Write the rational expression in radical form.

(x^3)^(3/2)

sqrt(x^9)

500

Write the rational expression in radical form.

(a^(4/5))/(a^(1/5))

root(5)(a^3)

Simplify

100

Simplify.  

32^(1/5)

2

200

Simplify.  

x^(7/8)/x^(5/8)

x^(1/4)

300

Simplify.

b^(4/9)*b^(5/9)

b

400

Simplify.

(y^(1/4))^(3/5)

y^(3/20)

500

Simplify.

(-64x^3)^(2/3)

16x^2

Find the inverse

100

The inverse of y = 2x + 4.

 y = 1/2 x - 2?

200

The inverse of y = 1/3 x + 2

y = 3x - 6?

300

The inverse of y = 5x² 

y = √ 1/5 y

400

The inverse of y = x³ + 2.

³√ y - 2?

500

Two functions that are inverses result in this value when function composition is applied.

x

Graph Transformations

100

The resulting function when y = √x is shifted two units up.

 y = √x  + 2?

200

The resulting function when y = ³√x is shifted three units right.

y = ³√(x - 3) ?

300

The resulting function when y = √x is reflected about the x-axis and streched by a factor of 4.

y = -4 √x ?

400

The resulting funtion when y = ³Vx is shifted up 5 units and shifted right 1 unit.

y = ³√(x - 1)  + 5 ?

500

The resulting function when y = √x is compressed by a factor of 1/2, shifted 7 units down and shifted 5 units left.

 y = 1/2 √(x+5) - 7 ?