WAEC Mathematics 2016 Paper

Concept:Convert all numbers to the same base, then simplify the exponents.Explanation:Write $27$ and $81$ as powers of $3$: $27 = 3^3$ and $81 = 3^4$.Substitute into the expression:$$\frac{3^{n-1} \times 27^{n+1}}{81^{n}} = \frac{3^{n-1} \times (3^3)^{n+1}}{(3^4)^n}$$Use the power rule $(a^m)^n = a^{mn}$:$$\frac{3^{n-1} \times 3^{3n+3}}{3^{4n}}$$Since the bases are the same, add the exponents in the numerator and subtract the denominator exponent:$$3^{(n-1) + (3n+3) - 4n}$$Simplify the exponent:$$n - 1 + 3n + 3 - 4n = 2$$Thus, the expression simplifies to:$$3^2 = 9$$Answer:$9$The correct option is B. $9$