Roots & Exponents

Question 1

Perfect Squares to Memorize

Answer 1

0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225

Question 2

Perfect Cubes to Memorize

Answer 2

0, 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000

Question 3

Non-perfect Square Roots to Memorize

Answer 3

Question 4

Multiplying Radicals

Answer 4

Question 5

Dividing Radicals

Answer 5

Question 6

Addition and Subtraction of Radicals

Answer 6

Question 7

Taking the Square Root of a Number and/or Binomial

Answer 7

Question 8

Exponents to Memorize: Bases of 2

Answer 8

Question 9

Exponents to Memorize: Bases of 3

Answer 9

Question 10

Exponents to Memorize: Bases of 4

Answer 10

Question 11

Exponents to Memorize: Bases of 5

Answer 11

Question 12

Multiplication of Like Bases

Answer 12

Question 13

Division of Like Bases

Answer 13

Question 14

Power to a Power Rule

Answer 14

Question 15

Multiplication of Different Bases and Like Exponents

Answer 15

Question 16

Division of Different Bases and Like Exponents

Answer 16

Question 17

Radicals Can Be Expressed in Exponential Form

Answer 17

Question 18

Multiple Square Roots

Answer 18

Question 19

Nonzero Base Raised to the Zero Power

Answer 19

When a nonzero base is raised to the zero power, the expression equals 1

Question 20

Any Base Raised to the 1st Power

Answer 20

When a base is raised to the first power, the value of the expression is simply that base

Question 21

Raising a Base to a Negative Exponent

Answer 21

Question 22

Addition and Subtraction of Like Bases

Answer 22

When adding or subtracting expressions with exponents, consider factoring out common factors

Question 23

Addition and Subtraction of Like Radicals

Answer 23

Question 24

Special Addition Rule with Exponents

Answer 24

Question 25

Number Properties of Exponents: Case #1

Answer 25

Base: greater than 1 Exponent: even positive integer

Question 26

Number Properties of Exponents: Case #2

Answer 26

Base: greater than 1 Exponent: odd positive integer greater than 1

Question 27

Number Properties of Exponents: Case #3

Answer 27

Base: less than -1 Exponent: even positive integer

Question 28

Number Properties of Exponents: Case #4

Answer 28

Base less than -1 Exponent: odd positive integer greater than 1

Question 29

Number Properties of Exponents: Case #5

Answer 29

Base: positive proper fraction Exponent: even positive integer

Question 30

Number Properties of Exponents: Case #6

Answer 30

Base: negative proper fraction Exponent: even positive integer

Question 31

Number Properties of Exponents: Case #7

Answer 31

Base: positive proper fraction Exponent: odd positive integer greater than 1

Question 32

Number Properties of Exponents: Case #9

Answer 32

Base greater than 1 Exponent: positive proper fraction

Question 32

Number Properties of Exponents: Case #8

Answer 32

Base: negative proper fraction Exponent: odd postive integer greater than 1

Question 33

Square Roots of Large Perfect Squares

Answer 33

When a perfect square ends with an even number of zeros, the quare root of such a perfect square will have exactly half the number of zeros to the right of the final to the right of the final nonzero digit as the perfect square

Question 34

Square Roots of Small Perfect Squares

Answer 34

If a decimal with a finite number of decimal places is a perfect square, its square root will have exactly half of the number of decimal places. Thus, a perfect square decimal must have an even number of decimal places.

Question 35

Cube Roots of Large Perfect Cubes

Answer 35

The cube root of a perfect cube integer has exactly one-third of the number of zeros to the right of the final nonzero digit as the orginal perfect cube

Question 36

Cube Roots of Small Perfect Cubes

Answer 36

The cube root of a perfect cube decimal has exactly one-third of the number of decimal places as the original perfect cube