JAMB Mathematics 2017 Paper

Concept:Rewrite every term using the same base, $3$, then combine the exponents.Explanation:First, express $27$ and $81$ as powers of $3$.$27 = 3^3$ and $81 = 3^4$.Substitute these into the given expression.$$3^{n-1} \times \frac{(3^3)^{n+1}}{(3^4)^n}$$Use the power rule to multiply the exponents.$$3^{n-1} \times \frac{3^{3(n+1)}}{3^{4n}}$$Since all bases are now $3$, add the exponents in the numerator and subtract the exponent in the denominator.$$3^{(n-1) + 3(n+1) - 4n}$$Simplify the powers:$n - 1 + 3n + 3 - 4n = 2$.Therefore, the expression becomes $3^2 = 9$.Answer:$9$