b. \( 3 x^{2} \cdot 5 x^{3} \)

To simplify the expression \( 3 x^{2} \cdot 5 x^{3} \), you multiply the coefficients (the numbers in front) and add the exponents of like bases. So, \( 3 \cdot 5 = 15 \) and \( x^{2} \cdot x^{3} = x^{(2+3)} = x^{5} \). Thus, \( 3 x^{2} \cdot 5 x^{3} = 15 x^{5} \). Math isn't just about numbers; it's a universal language that transcends cultures. Historically, the principles of algebra emerged in diverse ancient civilizations, from the Babylonians who solved equations on clay tablets to the Arab mathematicians who introduced systematic algebra. This rich history is a testament to the human quest for understanding and organizing the chaos of numbers. In the real world, mastering algebra is essential; it’s not just found in textbooks. Whether calculating areas when remodeling your home, budgeting finance, or even analyzing trends in data, algebraic expressions appear everywhere! Understanding algebra helps navigate day-to-day challenges and boosts problem-solving skills that are crucial in various fields, from engineering to economics.