AMC 8 2026 (Problem 9)What is the value of this expression?16818116\frac{\sqrt{16\sqrt{81}}}{\sqrt{81\sqrt{16}}}81161681(A) 49\text{(A)}\;\frac49(A)94(B) 23\text{(B)}\;\frac23(B)32(C) 1\text{(C)}\;1(C)1(D) 32\text{(D)}\;\frac32(D)23(E) 94\text{(E)}\;\frac94(E)49Hints (3)Hint 11681=16×9=16×9=4×3=12\sqrt{16\sqrt{81}}=\sqrt{16\times9}=\sqrt{16}\times\sqrt9=4\times3=121681=16×9=16×9=4×3=12Hint 28116=81×4=81×4=9×2=18\sqrt{81\sqrt{16}}=\sqrt{81\times4}=\sqrt{81}\times\sqrt4=9\times2=188116=81×4=81×4=9×2=18Hint 3By Hints 1 and 2,Ans=16818116=1218=23\text{Ans}=\frac{\sqrt{16\sqrt{81}}}{\sqrt{81\sqrt{16}}}=\frac{12}{18}=\frac23Ans=81161681=1812=32Final Answer(B) 23\frac2332