Simplify \(\frac{5^x \times 25^{x - 1}}{125^{x + 1}}\)
A
52x + 1
B
5x + 1
C
5-5
D
52
E
53
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
\(\frac{5^x \times 25^{x - 1}}{125^{x + 1}}\) = \(\frac{5^x \times 5^{2x - 2}}{5^{3x + 3}}\)
= \(\frac{5^{x + 2x - 2}}{5^{3x + 3}}\)
= \(\frac{5^{3x - 2}}{5^{3x + 3}}\)
= 5\(^{3x - 2 - 3x - 3}\)
= 5\(^{-5}\)
Source: Myschool Past Questions Archive (Record #32658)