Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 5 - Exponents and Polynomials - 5.2 - Multiplying Monomials - Problem Set 5.2: 74

Answer

$144x^{10}y^{6}$

Work Step by Step

Using the laws of exponents, the given expression, $ (3xy)^2(2x^2y)^4 ,$ simplifies to \begin{array}{l}\require{cancel} \left( 3^{1(2)}x^{1(2)}y^{1(2)} \right)\left( 2^{1(4)}x^{2(4)}y^{1(4)}\right) \\\\= \left( 3^{2}x^{2}y^{2} \right)\left( 2^{4}x^{8}y^{4}\right) \\\\= \left( 9x^{2}y^{2} \right)\left( 16x^{8}y^{4}\right) \\\\= (9)(16)x^{2+8}y^{2+4} \\\\= 144x^{10}y^{6} .\end{array}
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