If \(5^{(x + 2y)} = 5\) and \(4^{(x + 3y)} = 16\), find \(3^{(x +...

If \(5^{(x + 2y)} = 5\) and \(4^{(x + 3y)} = 16\), find \(3^{(x + y)}\).

\(5^{(x + 2y)} = 5\)

∴ x + 2y = 1.....(i)

\(4^{(x + 3y)} = 16 = 4^2\)

x + 3y = 2 .....(ii)

x + 2y = 1.....(i)

x + 3y = 2......(ii)

y = 1

Substitute y = 1 into equation (i)

\(x + 2y = 1 \implies x + 2(1) = 1\)

\(x + 2 = 1 \implies x = -1\)

\(\therefore 3^{(x + y)} = 3^{(-1 + 1)}\)

\(3^{0} = 1\)

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