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

• 1

  Which of the following expressions is equivalent to ∛(x³) * ∛(x³)?

  回答

  (C)

  x²
• 2

  Simplify (x²)³ * x⁴

  回答

  (B)

  x¹⁰
• 3

  Solve for x: (1/4)^x=16

  回答

  (A)

  -2
• 4

  If x^-2 = 1/9, what is the value of x?

  回答

  (B)

  3
• 5

  If 2^x = 0.25, what is x?

  回答

  (A)

  -2
• 6

  Simplify the expression (x³y^-2) / (xy)

  回答

  (A)

  x²y^-3
• 7

  What is the solution to the equation 4^x * 4³ = 4⁵?

  回答

  (B)

  2
• 8

  Simplify √75 - √12

  回答

  (B)

  3√3
• 9

  Which of the following is equivalent to 16^0.75?

  回答

  (B)

  12
• 10

  Which of the following expressions is equivalent to 3^x+2?

  回答

  (D)

  3^x * 3²
• 11

  Which property of exponents is demonstrated by (x^m)ⁿ = x^m*n?

  回答

  (C)

  Power of a power
• 12

  If 5^x = 125, then what is the value of x+2?

  回答

  (C)

  5
• 13

  Solve for x: 2^x = 1/8

  回答

  (A)

  -3
• 14

  Simplify the expression (9x⁴y²)^1/2

  回答

  (A)

  3x²y
• 15

  Which of the following is the simplified form of (x²y³)⁴?

  回答

  (B)

  x⁸y¹²
• 16

  The expression (a³b^-2) / (a²b³) simplifies to:

  回答

  (B)

  a/b⁵
• 17

  Simplify (2x²) * (3x³)

  回答

  (B)

  6x⁵
• 18

  What is the result of simplifying 8^2/3?

  回答

  (B)

  4
• 19

  What is the value of x in the equation 4^x = 64?

  回答

  (B)

  3
• 20

  Which expression is equivalent to √(x⁴)?

  回答

  (B)

  x²
• 21

  Which of the following is a correct representation of the law of indices for the multiplication of powers with the same base?

  回答

  (B)

  a^m * aⁿ = a^m+n
• 22

  What is the expanded form of (a + b)²?

  回答

  (B)

  a² + 2ab + b²
• 23

  If 2^x * 2³ = 32, what is x?

  回答

  (B)

  2
• 24

  What is the simplified form of x^a * x^b * x^c?

  回答

  (B)

  x^a+b+c
• 25

  Which of the following are equal to 1?

  回答

  A

  B
• 26

  What is the value of (1000)^1/3?

  回答

  (A)

  10
• 27

  Simplify 3x² * 2x³

  回答

  (B)

  6x⁵
• 28

  What does a negative exponent indicate?

  回答

  (D)

  Reciprocal
• 29

  The expression ∛(8x⁶) is equivalent to:

  回答

  (A)

  2x²
• 30

  Simplify (4x²y^-3) / (2xy²)

  回答

  (A)

  2xy^-5
• 31

  What is the value of \((\frac{1}{5})^0\)?

  回答

  (B)

  1
• 32

  Simplify \( 5^0 + 5^1 \).

  回答

  (D)

  6
• 33

  Which expressions are equivalent to \( \frac{a^m}{a^n} \)? (Select all that apply)

  回答

  A

  C
• 34

  Which statement is true regarding the expression (a^x * a^y)?

  回答

  (C)

  It is equivalent to (a^{x+y})
• 35

  Which of the following statements is/are true about \(a^{-2}\)? (Select all that apply)

  回答

  (A)

  It is equivalent to \( \frac{1}{a^2} \)
• 36

  Which is a simplified form of ((a^2b)^3)?

  回答

  (B)

  (a^6b^3)
• 37

  Find *x*: (10^x = 0.1).

  回答

  (B)

  -1
• 38

  Which expression is equivalent to ( x^a * x^b )?

  回答

  (C)

  (x^{a+b})
• 39

  Simplify ( (2x^3)^2 ).

  回答

  (B)

  (4x^6)
• 40

  Which of the following is true about ( a^{-n} )?

  回答

  (B)

  It is equivalent to \(\frac{1}{a^n}\)
• 41

  Which value is equal to ( 27^{rac{1}{3}} )?

  回答

  (A)

  3
• 42

  What is the value of ( (rac{1}{3})^{-2} )?

  回答

  (D)

  9
• 43

  Simplify (3^2 + 3^0).

  回答

  (B)

  10
• 44

  What is the value of *x* if (4^x = 16)?

  回答

  (B)

  2
• 45

  Which of the following equals to ((rac{2}{3})^2)?

  回答

  (A)

  (rac{4}{9})
• 46

  Which expression is equivalent to ( 4^x = 64 )?

  回答

  (B)

  x = 3
• 47

  Which of the following represents a negative exponent?

  回答

  (C)

  (a^{-1})
• 48

  Which expression is equivalent to ((4x^2y^3)^0)?

  回答

  (B)

  1
• 49

  Simplify ( x^3 y^2 * x^2 y^3 ).

  回答

  (A)

  (x^5 y^5)
• 50

  Simplify (sqrt[3]{27x^6})

  回答

  (A)

  (3x^2)