If \(2^n = 128\), find the value of \(2^{n - 1})(5^{n - 2})\)
A
5(106)
B
2(106)
C
5(105)
D
2(105)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(2^n\) = 128
\(2^n = 2^7\)
n = 7
(2\(^{n - 1}\))(5\(^{n - 2}\)), then, put n = 7
= (2\(^{7 - 1}\))(5\(^{7 - 2}\))
= (\(2^6\))(\(2^5\))
= \(2^1 \times 2^5 \times 2^5\)
= 2 x (\(2 \times 5)^5\)
= 2(\(10^5\))
Source: Myschool Past Questions Archive (Record #36366)