Alg II Quiz review

Simplify the Rational Exponent

100

64^(2/3)

(64^(1/3))^2 = 4^2 = 16

200

4^(5/2)

(4^(1/2))^5 = 2^5 = 32

300

(-125)^(2/3)

(-125)^(2/3) = ((-125)^(1/3))^2 = (-5)^2 = 25

400

-27^(4/3)

-(27^(1/3))^4 = -(3)^4 = -(81) = -81 

500

(64/125)^(-2/3)

(64/125)^(-2/3) = (64/125)^((1/3)*2*(-1) = (((64/125)^(1/3))^2)^(-1) = ((4/5)^2)^(-1) = (16/25)^(-1) = 25/16

Roots

100

sqrt(49)

7

200

-sqrt(25)

-5

300

root(3)(-125)

-5

400

root(3)27 + sqrt(144)

15

500

root(5)32-root(10)1024

0

Exponents

100

write x*x*x*x in the form x^n, where n is a number

x⁴

200

Evaluate.

5^-3

1/125

300

Write with positive exponents.

x^-6

1/x^6

400

Write with positive exponents.

3x^-4y²

(3y^2)/x^4

500

Write with positive exponents.

((2*x^3)^0)/(xy)

1/(xy)

Definitions

100

What are the integers?

The integers are the whole numbers and their opposites.

200

What is a set?

A set is a collection of things.

300

What is a rational number?

A rational number is a number that can be written as a fraction of two integers.

400

What is an irrational number?

An irrational number is a number that cannot be written as a fraction of two integers.

500

What is an imaginary number?

An imaginary number is a number that can written as a product of a real number and 

sqrt(-1)

Set classification

100

Classify.

sqrt2

Irrational

200

Classify.

-5

Integer

Rational

300

Classify.

2

Natural Number

Whole Number

Integer

Rational Number

400

Classify  

sqrt25

Natural

Whole

Integer

Rational

500

Classify.

- (root 3 8)

Integer

Rational