Exponents and Roots: Master the Basics with Interactive Quizzes

Question 1

Which of the following expressions is in simplest radical form?

Accepted Answer

2√3

Answer

√12

Answer

6√2

Answer

10√3

Question 2

Simplify the expression (sqrt(3) + sqrt(5))/(sqrt(3) - sqrt(5)).

Accepted Answer

sqrt(3) - sqrt(5)

Answer

sqrt(3) + sqrt(5)

Answer

3 + 5

Answer

3 - 5

Question 3

Simplify the expression: (3^2) ^ -3

Accepted Answer

1/9

Answer

9

Answer

3/9

Answer

27

Question 4

Which of the following is the simplified form of (√x)^4?

Accepted Answer

x^8

Answer

x^2

Answer

x^4

Answer

x^(1/2)

Question 5

Evaluate the radical: √25

Accepted Answer

5

Answer

4

Answer

10

Answer

2

Question 6

Which expression is equivalent to (x^3)^4?

Accepted Answer

x^24

Answer

x^7

Answer

x^12

Answer

x^20

Question 7

Rationalize the denominator of 1 / (2 + sqrt(5)).

Accepted Answer

2 + sqrt(5) / 9

Answer

2 - sqrt(5) / 9

Answer

4 - 5 / 9

Answer

4 + 5 / 9

Question 8

Which of the following is not a property of radicals?

Accepted Answer

√(a + b) = √a + √b

Answer

√(a * b) = √a * √b

Answer

√(a^2) = a

Answer

√(1/a) = 1/√a

Question 9

Simplify the expression √(x^2y^4). What is the answer?

Accepted Answer

x^2y^2

Answer

xy^2

Answer

x^3y^2

Answer

x^4y^2

Question 10

Rationalize the denominator: 1/√2

Accepted Answer

√2/2

Answer

√2

Answer

1/2

Answer

2/√2

Question 11

Simplify: (27^(1/3))^(1/3)

Accepted Answer

3

Answer

9

Answer

27

Answer

81

Question 12

Simplify the expression: (2³)^4

Accepted Answer

2¹²

Answer

4⁷

Answer

8¹²

Answer

2⁷

Question 13

Which expression is the conjugate of 3 - √7?

Accepted Answer

3 + √7

Answer

-3 + √7

Answer

3 √7

Answer

-3 - √7

Question 14

Rationalize the denominator of the expression: 1 / (√3 - 1)

Accepted Answer

√3 + 1

Answer

1 - √3

Answer

√3 - 1

Answer

3 + 1

Question 15

Simplify the expression: (2^3)^4

Accepted Answer

2^12

Answer

2^6

Answer

8^12

Answer

4^12

Question 16

Simplify the expression: (a^2b^3)^(-1)

Accepted Answer

a^(-2)b^(-3)

Answer

ab^(-3)

Answer

a^(-2)b^(-1)

Answer

a^2b^3

Question 17

Rationalize the denominator of the expression: 1 / √5

Accepted Answer

√5 / 5

Answer

1 / 5

Answer

√5 / 1

Answer

5 / √5

Question 18

Which of the following expressions is undefined?

Accepted Answer

0^0

Answer

(-1)^0

Answer

1^0

Answer

2^0

Question 19

What is the simplified form of 2³ * 2⁵?

Accepted Answer

2⁸

Answer

2¹⁵

Answer

8²

Answer

2²

Question 20

Simplify the expression (x²/y³)^-2.

Accepted Answer

y⁶ / x⁴

Answer

x⁴ / y⁶

Answer

y³ / x²

Answer

x⁶ / y⁴

Question 21

Calculate the value of √(16 * 25).

Accepted Answer

20

Answer

10

Answer

40

Question 22

Simplify the radical expression √72.

Accepted Answer

6√2

Answer

8√2

Answer

36

Answer

2√6

Question 23

Which of the following expressions is NOT a true property of radicals?

Accepted Answer

√(a + b) = √a + √b

Answer

√(a²) = a

Answer

√(1/a) = 1/√a

Answer

√(ab) = √a * √b

Question 24

Rationalize the denominator of the expression 1/√5.

Accepted Answer

√5 / 5

Answer

5√5

Answer

5 / √5

Answer

√5 / 25

Question 25

Solve the equation x^(1/2) - 4 = 0 for x.

Accepted Answer

x = 16

Answer

x = 8

Answer

x = 4

Answer

x = 2

Question 26

What is the simplified form of (2x)^(1/3)?

Accepted Answer

2^(1/3) * x^(1/3)

Answer

x^(2/3)

Answer

2 / x^(1/3)

Answer

2x^(1/2)

Question 27

Simplify the radical expression √(x² + 2x + 1).

Accepted Answer

(x + 1)

Answer

Cannot be simplified

Answer

(x - 1)

Answer

(x² + 2x - 1)