Exponents and Powers

34. The value for (–7)⁶ ÷ 7⁶ is

• (A) 0
• (B) 1
• (C) –1
• (D) 7

33. The value of [1^–2 + 2^–2 + 3^–2] × 6² is

• (A) 32
• (B) –32
• (C) –31
• (D) 31

32. On dividing 8 by which number give the quotient 8⁵?

• (A) 8⁵
• (B) 8⁴
• (C) 8⁶
• (D) 8^–4

31. Which among the following is the correct representation of 24.58?

• (A) 2 × 10 + 4 × 1 + 5 × 10 + 8 × 1/100
• (B) 2 × 10 + 4 × 1 + 5 × 1/10 + 8 × 100
• (C) 2 × 10 + 4 × 1 + 5 × 1/10 + 8 × 1/100
• (D) 2 × 10 + 4 × 1 + 5 × 1/10 + 8 × 1/1000

30. Which among the following is the correct representation of 329.25?

• (A) 3 × 10² + 2 × 10¹ + 9 × 10⁰ + 2 × 10^–1 + 5 × 10^–2
• (B) 3 × 10² + 2 × 10¹ + 9 × 10⁰ + 2 × 10^–0 + 5 × 10^–1
• (C) 3 × 10² + 2 × 10¹ + 9 × 10⁰ + 2 × 10^–0 + 5 × 10^–2
• (D) 3 × 10² + 2 × 10¹ + 9 × 10⁰ + 2 × 10^–1 + 5 × 10^–3

29. What is the value of (–5)^–2 × (–5)^–3?

• (A) (–5)^–5
• (B) (–5)^–6
• (C) (–5)^–1
• (D) (–5)¹

28. What is the value of (–4)^–4 × (4)^–1?

• (A) 4⁵
• (B) 4^–5
• (C) 4^–4
• (D) 4³

27. What is the value of (–7)^–4 × (–7)²?

• (A) (7)⁵
• (B) (–7)^–2
• (C) (–7)^–2
• (D) (–7)^–2

26. The expression for 4^–3 as a power with the base 2 is

• (A) 2⁶
• (B) 2^–6
• (C) 2^–3
• (D) 2^–8

25. The expression for 8^–2 as a power with the base 2 is

• (A) 2⁶
• (B) 2^–6
• (C) 2^–3
• (D) 2^–8

24. If a⁶ × a⁵ × a⁰ = a^p, the value of p is

• (A) 12
• (B) 11
• (C) 0
• (D) 30

23. If 5^x × 5³ = 5⁶, the value of x is

• (A) –1
• (B) 0
• (C) 3
• (D) 1

22. If 5^x = 5³ × 5⁶, the value of x is

• (A) 3
• (B) 0
• (C) 9
• (D) 10

21. If u = (–1)²⁰²² and v = (–1)²⁰²³, then u + v is equal to

• (A) 0
• (B) 2
• (C) –1
• (D) 1

20. If u = (–1)²⁰²² and v = (–1)²⁰²³, then u × v is equal to

• (A) –1
• (B) 2
• (C) 3
• (D) 1

19. If u = (–1)²⁰²² and v = (–1)²⁰²³, then which among the following is true?

• (A) u = v
• (B) u > v
• (C) u < v
• (D) None of these

18. What is the value of x so that (–2)³ × (–2)^–6 = (–2)^2x–1?

• (A) –1
• (B) –2
• (C) –3/2
• (D) –1/2