If 2n = y, Find 2$^{(2 + \frac{n}{3})}$

Analyze the question: The statement "2n = y" is most likely a typing error for 2^n = y (the original WASSCE question is 2^n = y). We need to find 2^(2 + n/3) in terms of y.

If it literally meant 2n = y, then n = y/2 and the answer would be 2^(2 + y/6), which matches none of the options. So the intended condition is 2^n = y.

Concept: Laws of indices:

• a^(m+n) = a^m × a^n
• a^(mn) = (a^m)^n

Solution:

2^(2 + n/3) = 2² × 2^(n/3)

Now 2^(n/3) = (2^n)^(1/3) = y^(1/3)

So:

2^(2 + n/3) = 4 × y^(1/3) = 4y^(1/3)

Tip: When you see a sum in the power, split it into a product of separate powers. When you see a fraction in the power, rewrite it as a root of the known expression. Here, 2^(n/3) is just the cube root of 2^n.