17. IAR Review: No Calculator What is the value of \( x^{4}+0.5 y^{3} \) when \( x=2 \) and \( y=4 \)

To find the value of \( x^{4} + 0.5 y^{3} \) when \( x = 2 \) and \( y = 4 \), we start by calculating each term separately: 1. Calculate \( x^{4} \): \[ 2^{4} = 16 \] 2. Calculate \( 0.5 y^{3} \): \[ 0.5 \times 4^{3} = 0.5 \times 64 = 32 \] Now, combine the two results: \[ 16 + 32 = 48 \] So, the value of \( x^{4} + 0.5 y^{3} \) is \( \boxed{48} \). Get this: mathematical expressions like the one above aren't just formulas—they're gateways to understanding how quantities relate to one another. It's a bit like baking a cake! Just as each ingredient plays its role in creating a delicious treat, each term adds to the final value. If you're intrigued by these calculations, consider diving into algebra textbooks or online resources that provide a variety of problems. They'll challenge your skills and expand your problem-solving toolkit in no time!