faluate the expression when \( a=6 \). \( a^{2}-19 \)

To evaluate the expression \( a^{2} - 19 \) when \( a=6 \), we first substitute 6 for \( a \). This gives us: \( 6^{2} - 19 = 36 - 19 = 17 \). So, the value of the expression is 17. Now, isn’t it fascinating how squaring a number has such impactful results? In this case, going from \( a \) to \( a^2 \) transformed a simple number into a larger one, allowing us to explore its relationship with subtraction. It’s like a mathematical journey—6 takes a leap to 36, and then we subtract to land at 17! If you're ever curious about the power of exponents, you can dive into some math history. The concept of squaring dates back to ancient civilizations where it was used in land measurement. The Babylonians already had methods for calculating areas, which involved squaring, making it a foundational principle that has shaped mathematics as we know it today.