If 2n = 128, find the value of (2n – 1)(5n – 1)

If 2ⁿ = 128, find the value of (2^{n – 1})(5^{n – 1})

Correct Answer: Option D

Explanation

2ⁿ = 128
2ⁿ = 2⁷
n = 7
(2^{n – 1})(5^{n – 2}) = (2^{n – 2}.2)(5^{n – 2}) put n = 7
(2^{n – 1})(5^{n – 2}) = 2(2^{n – 2} x 5^{n – 2})
= 2(2 x 5)^{n – 2}
= 2(10^{n – 2}) put n = 7
(2^n-1)(5^n-2) = 2(10⁵)