\( \Rightarrow x ^ { 3 } \cdot 2 x ^ { 3 } \cdot x \)

To multiply \( x^3 \cdot 2x^3 \cdot x \), you first combine the coefficients and the variables separately. Here, \( 2 \) is the coefficient, and for the variables, you add their exponents since they have the same base. So, \( x^3 \cdot x^3 \cdot x = x^{3+3+1} = x^7 \). Therefore, you get \( 2x^7 \) as the final result! Now, let's break down why we're allowed to add the exponents: it's due to the properties of exponents, which state that when multiplying like bases, you simply add the exponents together! This rule allows math to stay organized and succinct, ensuring calculations remain straightforward. Fun fact: this principle can be traced back to ancient civilizations like the Greeks and Babylonians who laid the groundwork for modern algebra!