Master Exponents and Radicals: Conquer Powers and Roots in Mathematics

Question 1

A city's population grows by 2% each year. If the population starts at 50,000, what will it be in 10 years?

Accepted Answer

60,496

Answer

45,000

Answer

55,000

Answer

80,000

Question 2

Simplify the square root expression: √(x²y⁴)

Accepted Answer

xy²

Answer

x²y⁴

Answer

x⁴y²

Answer

(xy)²

Question 3

Simplify √9:

Accepted Answer

3

Answer

9

Answer

6

Answer

0

Question 4

Find the value of 4^-3:

Accepted Answer

0.015625

Answer

0.25

Answer

0.0625

Question 5

Evaluate (8)^(2/3):

Accepted Answer

4

Answer

16

Answer

8

Answer

2

Question 6

Find the square root of (x⁴y³)³:

Accepted Answer

x⁶y^(3/2)

Answer

x³y^(3/2)

Answer

x⁶y³

Answer

x³y³

Question 7

Which of the following is the conjugate of √7 - 3?

Accepted Answer

√7 + 3

Answer

√7 - 3

Answer

7 - 2√7

Answer

3 - √7

Question 8

Find the value of 3 to the power of negative 2

Accepted Answer

1/9

Answer

1/3

Answer

9

Question 9

Simplify the square root of 16

Accepted Answer

4

Answer

10

Answer

8

Answer

16

Question 10

Simplify the square root of 25x squared

Accepted Answer

5x

Answer

5x squared

Answer

25x

Question 11

Rationalize the denominator of the expression (square root of 2)/(square root of 3)

Accepted Answer

(square root of 2)(square root of 3)/3

Answer

square root of 6/3

Answer

square root of 3/2

Answer

square root of 2/3

Question 12

Which of the following expressions is equal to the square root of 81 divided by the square root of 16?

Accepted Answer

the square root of 81 divided by the square root of 16

Answer

81 divided by the square root of 16

Answer

16 divided by the square root of 81

Answer

square root of 81 multiplied by the square root of 16

Question 13

Simplify the expression: the cube root of 8

Accepted Answer

2

Answer

6

Answer

4

Answer

8

Question 14

Simplify the expression: the square root of 49

Accepted Answer

7

Answer

28

Answer

21

Answer

14

Question 15

Which of the following is equivalent to (x squared / y cubed) raised to the power of -2?

Accepted Answer

y raised to the power of 6 / x raised to the power of 4

Answer

x squared / y cubed

Answer

x raised to the power of 4 / y raised to the power of 6

Answer

y cubed / x squared

Question 16

Simplify the expression (2^3)^5:

Accepted Answer

2^15

Answer

2^12

Answer

2^24

Answer

2^8

Question 17

Find the value of 4^(-2):

Accepted Answer

1/16

Answer

-16

Answer

16

Answer

-1/16

Question 18

Simplify the expression (8^1/3)(2^1/3):

Accepted Answer

4^(1/3)

Answer

2^(1/3)

Answer

(4/2)^(1/3)

Question 19

Rationalize the denominator of the expression 1/√3:

Accepted Answer

√3/3

Answer

√3

Answer

3/√3

Answer

1/√3

Question 20

Evaluate the expression 2^0

Accepted Answer

1

Answer

2

Answer

undefined

Answer

0

Question 21

Simplify the expression √(121) multiplied by √(169)

Accepted Answer

39

Answer

18

Answer

13

Answer

21

Question 22

Simplify the expression: 2^3 * 2^5

Accepted Answer

2^8

Answer

16^5

Answer

2^2

Answer

4^8

Question 23

Simplify the expression: (5x^2)^3

Accepted Answer

125x^6

Answer

125x^5

Answer

25x^5

Answer

50x^6

Question 24

Which of the following is equivalent to (2^3)^2?

Accepted Answer

2^6

Answer

8^2

Answer

2^5

Answer

4^3

Question 25

Evaluate the expression: |3| + |4|

Accepted Answer

7

Answer

-7

Answer

3

Answer

6

Question 26

Which of the following is NOT a property of exponents?

Accepted Answer

a^-m = m/a

Answer

a^m * a^n = a^(m+n)

Answer

(a^m)^n = a^(m * n)

Answer

a^0 = 1

Question 27

Simplify the expression: (x³ * x⁵) / x²

Accepted Answer

x⁶

Answer

x³

Answer

x¹⁰

Answer

x¹⁵

Question 28

What is the value of 8^(2/3)?

Accepted Answer

4

Answer

16

Answer

64

Answer

2

Question 29

Simplify the radical expression: √(25x⁴y⁶)

Accepted Answer

5x²y³

Answer

√(25x⁴) * √(y⁶)

Answer

5x⁴y⁶

Answer

√(25) * √(x⁴) * √(y⁶)

Question 30

Which of the following is equivalent to (√a)²?

Accepted Answer

a

Answer

√(a²)

Answer

2√a

Answer

a²

Question 31

Solve for x: x^(1/2) = 5

Accepted Answer

25

Answer

√5

Answer

10

Answer

5

Question 32

Simplify the expression: (√2 + √3)(√2 - √3)

Accepted Answer

-1

Answer

5

Answer

1

Answer

2 - 3

Question 33

Which of the following is the simplest form of √(12) + √(27)?

Accepted Answer

5√3

Answer

√36

Answer

√(12) + √(27)

Answer

√(39)

Question 34

What is the value of ∛(27) + ∛(64)?

Accepted Answer

7

Answer

11

Answer

9

Answer

37

Question 35

Which of the following is equal to (x^(1/3))⁶?

Accepted Answer

x²

Answer

x⁶

Answer

x^(1/2)

Answer

x^(1/18)

Question 36

Simplify the expression: (√x / √y)³

Accepted Answer

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

Answer

(√x / √y)³

Answer

x³ / y³

Answer

√(x³ / y³)

Question 37

Evaluate the expression: 2^5

Accepted Answer

32

Answer

52

Answer

16

Answer

25

Question 38

Simplify the expression: (x^3)(x^4)

Accepted Answer

x^7

Answer

x^12

Answer

x^2

Answer

x^1

Question 39

Find the value of: √(144)

Accepted Answer

12

Answer

8

Answer

6

Answer

16

Question 40

Simplify the expression: (3√5)(2√2)

Accepted Answer

6√10

Answer

10√6

Answer

5√10

Answer

15√2

Question 41

Express 64 as a power of 2

Accepted Answer

2^6

Answer

2^4

Answer

2^3

Answer

2^8

Question 42

Find the value of: √(9/16)

Accepted Answer

3/4

Answer

3/8

Answer

9/16

Answer

1/4

Question 43

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

Accepted Answer

8x^6

Answer

2x^5

Answer

8x^5

Answer

4x^6

Question 44

Evaluate the expression: √(81 * √81)

Accepted Answer

27

Answer

18

Answer

81

Answer

9

Question 45

Find the value of: 2^0 + 3^0

Accepted Answer

2

Answer

1

Answer

5

Answer

6

Question 46

Simplify the expression: (√3 + √5)(√3 - √5)

Accepted Answer

-2

Answer

8

Answer

10

Answer

0