Thomas' Calculus 13th Edition

We alternatively defined $|x|$ as $|x|=\sqrt{x^{2}}$ Apply on $x=ab:$ $|ab|=\sqrt{(ab)^{2}}=\sqrt{a^{2}b^{2}}=\sqrt{a^{2}}\cdot\sqrt{b^{2}}=|a|\cdot|b|$