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