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: 75

Answer

$25x^{7}y^{8}$

Work Step by Step

Using the laws of exponents, the given expression, $ (5x^2y)^2(xy^2)^3 ,$ simplifies to \begin{array}{l}\require{cancel} \left( 5^{1(2)}x^{2(2)}y^{1(2)} \right)\left( x^{1(3)}y^{2(3)}\right) \\\\= \left( 5^{2}x^{4}y^{2} \right)\left( x^{3}y^{6}\right) \\\\= \left( 25x^{4}y^{2} \right)\left( x^{3}y^{6}\right) \\\\= 25x^{4+3}y^{2+6} \\\\= 25x^{7}y^{8} .\end{array}
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