Simplify \(\frac{5^x \times 25^{x - 1}}{125^{x + 1}}\)
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Correct Answer: Option C
Explanation:
\(\frac{5^x \times 25^{x - 1}}{125^{x +Â 1}}\) = \(\frac{5^x \times 5^{2x - 2}}{5^{3x +Â 3}}\)
= \(\frac{5^{x + 2x - 2}}{5^{3x +Â 3}}\)
= \(\frac{5^{3x - 2}}{5^{3x +Â 3}}\)
= 5\(^{3x - 2 - 3x -Â 3}\)
= 5\(^{-5}\)
\(\frac{5^x \times 25^{x - 1}}{125^{x +Â 1}}\) = \(\frac{5^x \times 5^{2x - 2}}{5^{3x +Â 3}}\)
= \(\frac{5^{x + 2x - 2}}{5^{3x +Â 3}}\)
= \(\frac{5^{3x - 2}}{5^{3x +Â 3}}\)
= 5\(^{3x - 2 - 3x -Â 3}\)
= 5\(^{-5}\)