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Simplify; \(\frac{3^{n - 1} \times 27^{n + 1}}{81^{n}}\)

Mathematics
WAEC 2016

Simplify; \(\frac{3^{n - 1} \times 27^{n + 1}}{81^{n}}\)
  • A. 32n
  • B. 9
  • C. 3n
  • D. 3n + 1
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Correct Answer: Option B
Explanation
\(\frac{3^{n - 1} \times 27^{n + 1}}{81^{n}}\)

= \(\frac{3^{n - 1} \times 3^{3(n + 1)}}{3^{4n}}\)

= 3\(^{n - 1 + 3n + 3 - 4n}\)

= 3\(^{4n - 4n - 1 + 3}\)

= 32

= 9

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