Chapter 4 - Polynomials - 4.1 Exponents and Their Properties - 4.1 Exercise Set - Page 236: 74

$50x^{13}$

Using $(ab)^x=a^xb^x$, then the expression, $ (5x^3)^2(2x^7) $, simplifies to \begin{array}{l}\require{cancel} (5^2x^{3(2)})(2x^7) \\\\= (25x^{6})(2x^7) .\end{array} Using $a^x\cdot a^y=a^{x+y}$, then the expression, $ (25x^{6})(2x^7) $, simplifies to \begin{array}{l}\require{cancel} 25\cdot2x^{6+7} \\\\= 50x^{13} .\end{array}