Final answer:
To demonstrate that 7 is a Mersenne prime, Ogechi should use the expression 2³ - 1, which equals 7, thus showing that 7 is indeed a Mersenne prime. So option (a) is correct.
Step-by-step explanation:
Ogechi is attempting to prove that 7 is a Mersenne prime. A Mersenne prime is a prime number of the form Mn = 2n - 1, where n is an integer. In order to show that 7 is a Mersenne prime, Ogechi should find a value of n such that 2n - 1 equals 7.
Exploring the options given:
(a) 2³-1 = 7
(b) 2⁴-1 = 15
(c) 2⁵-1 = 31
(d) 2⁶-1 = 63
Now, we can conclude that the correct expressions representing Mersenne primes are (a) 2³-1 and (c)
2⁵-1. Both expressions result in prime numbers (7 and 31) when evaluated, and the exponents (3 and 5) are prime numbers as well.
Therefore, to demonstrate that 7 is a Mersenne prime, Ogechi should use the expression 2³-1, so the correct answer is (a).