What is the value of this expression? \frac√16√81√81√16

2026 AMC 8 Problem 9 — Solution & Video

2026 AMC 8 Problem 9

Attempt Problem 9 of the 2026 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2026 AMC 8 solutions, or check the answer key.

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What is the value of this expression? $\frac{\sqrt{16\sqrt{81}}}{\sqrt{81\sqrt{16}}}$

$\dfrac{4}{9}$

$\dfrac{2}{3}$

$1$

$\dfrac{3}{2}$

$\dfrac{9}{4}$

Answer: B

Concepts:radical

Difficulty rating: 1040

Video solution:

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Written solution:

The numerator is $\sqrt{16\sqrt{81}}$ $=\sqrt{16\cdot9}$ $=\sqrt{144}$ $=12$ . The denominator is $\sqrt{81\sqrt{16}}$ $=\sqrt{81\cdot4}$ $=\sqrt{324}$ $=18$ . The value is $12/18=2/3$ .

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