250+ TOP MCQs on Number Theory and Cryptography Rules of Exponents

Basic Discrete Mathematics Questions and Answers on “Number Theory and Cryptography – Rules of Exponents”.

1. For some number b, (¹⁄_b)^-n is equal to _________
a) -bⁿ
b) n^b
c) bⁿ
d) none of the mentioned

Answer: c
Clarification: b^-1 reciprocal of b.

2. If ab = 1, where a and b are real numbers then?
a) a = b^-1
b) b = a
c) a = b = 2
d) none of the mentioned

Answer: a
Clarification: This means that a is inverse of b or b is inverse of a.

3. If a is a real number than a⁰ is defined as _________
a) 0
b) a
c) 1
d) -1

Answer: a
Clarification: Any number to the power zero is one.

4. For some number a, b and c, c^a x c^b is equal to _________
a) c^a-b
b) c^a+b
c) c
d) none of the mentioned

Answer: b
Clarification: If base are same then exponenents powers are added.

5. For some number a, b and c, c^a/c^b is equal to _________
a) c^a-b
b) c^a+b
c) c
d) None of the mentioned

Answer: a
Clarification: If base are same then exponenents powers are added, 1/c^b = c^-b.

6. State whether the given statement is true or false.
Exponentiation is commutative.
a) True
b) False

Answer: b
Clarification: A^b is not equal to b^A, exponentiation is not commutative.

7. State whether the given statement is true or false.
Exponentiation is associative.
a) True
b) False

Answer: b
Clarification: Exponentiation is not associative.

8. If 2^a-b = 1 then the value of a-b is equal to _________
a) 1
b) 0
c) 2
d) none of the mentioned

Answer: b
Clarification: 1 = 2⁰, so a-b = 0.

9. For some number a, b and c, a^c x b^c is equal to _________
a) (ab)^c
b) (ac)^b
c) (cb)^a
d) None of the mentioned

Answer: a
Clarification: If power are same then bases are multiplied.

10. If 0^a is not equal to zero then which of the values a cannot take _________
a) 1
b) 2
c) -1
d) 0

Answer: d
Clarification: a⁰ = 1, for any real number.