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Which of the following is not the reciprocal of (2/3)⁴? (a) (3/2)⁴ (b) (3/2)^-4 (c) (2/3)^-4 (d) 3⁴/2⁴

Answer: (b) (3/2)-4 In Mathematics, reciprocal means an expression which when multiplied by another expression, gives unity (1) as a result. The... View Article

Cube of -1/2 is (a) 1/8 (b) 1/16 (c) -1/8 (d) -1/16

Answer: (c) -1/8 In mathematics, the cube of the number represents the number, when the given number is multiplied thrice or three times. The... View Article

For a non-zero rational number z, (z^-2)³ equal to (a) z⁶ (b) z^-6 (c)z¹ (d) z⁴

Answer: (b) z-6 By the law of exponents: (am)n = amn (z-2)3 = z(-2 × 3) = z -6 An exponent of a number represents the number of times... View Article

For a non-zero rational number p, p¹³ ÷ p⁸ is equal to (a) p⁵ (b) p²¹ (c) p^-5 (d) p^-19

Answer: (a) p5 By law of exponent: (a)m÷(a)n = (a)m-n p13 ÷ p8 = p(13 - 8) = p(5) An exponent of a number represents the number... View Article

For any two non-zero rational numbers x and y, x⁴ ÷ y⁴ is equal to (a) (x ÷ y)⁰ (b) (x ÷ y)¹ (c) (x ÷ y)⁴ (d) (x ÷ y)⁸

Answer: (c) (x ÷ y)4 x4 ÷ y4 The law of exponent (a)m÷(b)m = (a÷b)m x4 ÷ y4 = (x ÷ y)4 An exponent... View Article

(3/4)⁵ ÷(5/3)⁵ is equal to (a) (3/4÷5/3)⁵ (b) (3/4 ÷ 5/3)¹ (c) (3/4 ÷ 5/3)⁰ (d) (3/4 ÷ 5/3)¹⁰

Answer: (a) (3/4÷5/3)5 (3/4)5 ÷(5/3)5 The law of exponent (a)m÷(b)m = (a÷b)m (3/4)5 ÷(5/3)5 = (3/4 ÷... View Article

(1/10)⁰ is equal to (a) 0 (b) 1/10 (c) 1 (d) 10

Answer: (c) 1 By law of exponent a0 = 1 ∴ (1/10)0 = 1 An exponent of a number represents the number of times the number is multiplied by... View Article

The usual form for 2.03 × 10^-5 (a) 0.203 (b) 0.00203 (c) 203000 (d) 0.0000203

Answer: (d) 0.0000203 Any number can be expressed as decimal numbers between 1 and 10 multiplied by a power of 10. This form of representation is... View Article

The standard form for 234000000 is (a) 2.34 × 10⁸ (b) 0.234 × 10⁹ (c) 2.34 × 10^-8 (d) 0.234×10^-9

Answer: (a) 2.34 × 108 Any number can be expressed as decimal numbers between 1 and 10 multiplied by a power of 10. This form of... View Article

The standard form for 0.000064 is (a) 64 × 10⁴ (b) 64 × 10^-4 (c) 6.4 × 10⁵ (d) 6.4 × 10^-5

Answer: (d) 6.4 × 10-5 Any number can be expressed as decimal numbers between 1 and 10 multiplied by a power of 10. This form of... View Article

The value of (7^-1 – 8^-1) -1 – (3^-1 – 4^-1)^-1 is: (a) 44 (b) 56 (c) 68 (d) 12

Answer: (a) 44 (7-1 – 8-1) -1 – (3-1 – 4-1)-1 = (1/7-1/8) -1 – (1/3-1/4)-1 = (1/56) -1 – (1/12) -1 = 56 – 12... View Article

For a non-zero integer x, (x⁴)^-3 is equal to: (a) x¹² (b) x^-12 (c) x⁶⁴ (d) x^-64

Answer: (b) x-12 (x4)-3 By the law of exponents: (am)n = amn = x4 × (-3) = x-12 An exponent of a number represents the number of times... View Article

For a non-zero integer x, x⁷ ÷ x¹² is equal to: (a) x⁵ (b) x¹⁹ (c) x^-5 (d) x^-19

Answer: (c) x-5 x7 ÷ x12 By the law of exponents: am ÷ an = am-n = x7-12 = x-5 An exponent of a number represents the number of... View Article

(–9)³ ÷ (–9)⁸ is equal to: (a) (9)⁵ (b) (9)^-5 (c) (– 9)⁵ (d) (– 9)^-5

Answer: (d) (– 9)-5 (–9)3 ÷ (–9)8 By the law of exponents: am ÷ an=am-n = (-9)3-8 = (-9)-5 An exponent of a... View Article

(-7/5)^-1 is equal to: (a) 5/7 (b) – 5/7 (c) 7/5 (d) -7/5

Answer: (b) – 5/7 (-7/5)-1 By the law of exponents: a-n = 1/an = 1/(-7/5) = -5/7 An exponent of a number represents the number of times... View Article

(-5/7)^-5 is equal to: (a) (5/7)^-5 (b) (5/7)⁵ (c) (7/5)⁵ (d) (-7/5)⁵

Answer: (d) (-7/5)5 (-5/7)-5 By the law of exponents: a-n = 1/an = 1/(-5/7)5 = (-7/5)5 An exponent of a number represents the number of times... View Article

Which of the following is equal to (-3/4)^-3? (a) (3/4)^-3 (b) – (3/4)^-3 (c) (4/3)³ (d) (-4/3)³

Answer: (d) (-4/3)3 (-3/4)-3 By the law of exponents: a-n = 1/an = 1/(-3/4)3 = (-4/3)3 An exponent of a number represents the number of times... View Article

If x be any integer different from zero and m, n be any integers, then (x^m)ⁿ is equal to: (a) x^m+n (b) x^mn (c) x^m/n (d) x^m-n

Answer: (b) xmn By the law of exponents (am)n = amn (xm)n = xmn An exponent of a number represents the number of times the number is... View Article

If x be any integer different from zero and m be any positive integer, then x^-m is equal to: (a) x^m (b) –x^m (c) 1/x^m (d) -1/x^m

Answer: (c) 1/xm By the law of exponents a-m = 1/am ∴ x-m = 1/xm An exponent of a number represents the number of times the number is... View Article

If x be any non-zero integer, then x^-1 is equal to (a) x (b) 1/x (c) – x (c) -1/x

Answer: (b) 1/x By the law of exponents a-m = 1/am ∴ x-1 = 1/x1 An exponent of a number represents the number of times the number is... View Article

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