Answer
See proof below.
Work Step by Step
We alternatively defined $|x|$ as
$|x|=\sqrt{x^{2}}$
Apply on $x=ab:$
$|ab|=\sqrt{(ab)^{2}}=\sqrt{a^{2}b^{2}}=\sqrt{a^{2}}\cdot\sqrt{b^{2}}=|a|\cdot|b|$
University Calculus: Early Transcendentals (3rd Edition)
by Hass, Joel R.; Weir, Maurice D.; Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0321999584
ISBN 13:
978-0-32199-958-0
Chapter Appendices - Section A.1 - Real Numbers and the Real Line - Exercises - Page AP-6: 25
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