1. Sadie should note that \(54a^7b^3\ge 0\) and if \(a\ge 0\), then \(b\ge 0\).
2. While simplifying Sadie makes some mistakes (it must be \(3^2\) instead of \(3^3\) and she missed the sign of absolute value for b). The right way to find the correct answer is:
\(\sqrt{54a^7b^3}=\sqrt{3^2\cdot 6\cdot a^2\cdot a^5\cdot b^2\cdot b} =3\cdot a\cdot |b| \sqrt{6\cdot a^5\cdot b}=3ab\sqrt{6a^5b}\).
3. The simpliest expression is \(3ab\sqrt{6a^5b} =3ab\sqrt{6\cdot a^2\cdot a^2\cdot a\cdot b} =3a^3b\sqrt{6ab}\).
