Mathematics for IGCSE & O level - Indices 2 (Section 1)

• 1

  Simplify (16x⁸)^1/4

  回答

  (B)

  4x²
• 2

  Which of the following is equivalent to (x^-1 + y^-1)?

  回答

  (C)

  1/x + 1/y
• 3

  Simplify (x^a * x^b) / x^c

  回答

  (B)

  x^a+b-c
• 4

  What is the value of (1/2)^-2?

  回答

  (D)

  4
• 5

  Simplify (x³)²

  回答

  (B)

  x⁶
• 6

  Which expression is the result of adding the exponents of a²b³ * a³b²

  回答

  (D)

  a⁵b⁶
• 7

  If 2^x = 16, what is the value of x?

  回答

  (C)

  4
• 8

  If a^x = b and b^y = c, which expression equals a^xy?

  回答

  (A)

  c
• 9

  Simplify: (4x³y²) / (2xy)

  回答

  (A)

  2x²y
• 10

  Which expression is equivalent to (2x)³?

  回答

  (C)

  8x³
• 11

  Simplify a² * b³ * a^-1 * b

  回答

  (B)

  ab⁴
• 12

  Simplify x^-3 / x^-5

  回答

  (C)

  x²
• 13

  If x³= 125, then x equals?

  回答

  (B)

  5
• 14

  What is the result when simplifying (a^1/2 * b^1/2)²?

  回答

  (A)

  ab
• 15

  Simplify the expression: 3⁴ * 3^-2

  回答

  (B)

  3²
• 16

  What is the value of (3²)^1/2?

  回答

  (A)

  3
• 17

  If a³ = 27, what is the value of a²?

  回答

  (C)

  9
• 18

  What is the value of 16^1/4?

  回答

  (A)

  2
• 19

  Find the value of x in the equation: (5^x)² = 625

  回答

  (B)

  3
• 20

  If 3^x = 81, what is x?

  回答

  (C)

  4
• 21

  Which of the following is equal to x^2/3?

  回答

  (B)

  ∛(x²)
• 22

  Simplify a⁵ / a²

  回答

  (A)

  a³
• 23

  Which is the simplified form of (x^1/2+y^1/2)²?

  回答

  (B)

  x + y + 2x^1/2y^1/2
• 24

  Solve for x: 2^2x = 16

  回答

  (B)

  2
• 25

  Simplify: (5^-2)^-1

  回答

  (C)

  25
• 26

  Select the simplified forms of the following expressions:

  回答

  A

  D
• 27

  Simplify (x^1/2) / (x^-1/2)

  回答

  (A)

  x
• 28

  Simplify: a⁵ / a²

  回答

  (B)

  a³
• 29

  Which of the following is equivalent to a⁰?

  回答

  (B)

  1
• 30

  Evaluate: 9^1/2 - 4^1/2

  回答

  (A)

  1
• 31

  Simplify 4^x + 4^x + 4^x + 4^x

  回答

  (C)

  4 * 4^x
• 32

  Simplify x⁴ / x^-2

  回答

  (B)

  x⁶
• 33

  The expression (x² - 4) can be factored as:

  回答

  (C)

  (x - 2)(x + 2)
• 34

  Simplify (x^a+b) / x^b

  回答

  (A)

  x^a
• 35

  Simplify (a^1/2 * a^1/3) / a^1/6

  回答

  (B)

  a
• 36

  Simplify: (3a²b)²

  回答

  (C)

  9a⁴b²
• 37

  Which of the following is equivalent to √20?

  回答

  (A)

  2√5
• 38

  If 4^x = 0.125, find the value of x.

  回答

  (A)

  -3/2
• 39

  Solve for x: 9^x = 27

  回答

  (B)

  1.5
• 40

  Express √(9x⁴) in simplest form.

  回答

  (A)

  3x²
• 41

  Solve the equation: 3^x-1 = 9

  回答

  (C)

  3
• 42

  What is the simplified form of √x * √y?

  回答

  (A)

  √(xy)
• 43

  Simplify: (a³b²)^-1

  回答

  (A)

  a^-3b^-2
• 44

  What is the result when you simplify (a^m/aⁿ) * aⁿ?

  回答

  (A)

  a^m
• 45

  What is the simplified form of the expression √a * √a * a?

  回答

  (A)

  a²
• 46

  What is the value of (1/27)^-1/3?

  回答

  (D)

  3
• 47

  What is the value of 4^3/2?

  回答

  (B)

  8
• 48

  What is the value of x when x^-2 = 4?

  回答

  (B)

  -0.5
• 49

  What is the result when simplifying √2 * √8?

  回答

  (C)

  4
• 50

  Which of the following is NOT a correct application of the laws of indices?

  回答

  (C)

  z⁶ / z² = z³