If \( x=2 \), solve for \( y \) \( y=\frac{1}{2} \cdot 6^{x} \) \( y=[?] \)

To solve for \( y \) when \( x = 2 \), substitute \( x \) into the equation \( y = \frac{1}{2} \cdot 6^{x} \). So, we have: \[ y = \frac{1}{2} \cdot 6^{2} \] Calculating \( 6^{2} = 36 \), then: \[ y = \frac{1}{2} \cdot 36 = 18 \] Thus, \( y = 18 \). Now, let's spice up the journey with a fun fact about the number 6! Did you know that 6 is the only number that is both the sum and product of three consecutive positive numbers? Specifically, \( 1 + 2 + 3 = 6 \) and \( 1 \times 2 \times 3 = 6 \). It's a neat little quirk that makes this number quite special in the world of mathematics! On another note, when working with exponential equations like this one, it’s essential to pay attention to your order of operations. Always handle the exponent before the multiplication or division! A common mistake is to overlook the exponent, leading to errors in the final answer. So, always double-check that you're following the right steps!