1993 AMC 12 Problem 6

Attempt Problem 6 of the 1993 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1993 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

\sqrt{\frac{8^{10}+4^{10}}{8^4+4^{11}}}=

\sqrt2

16

32

12^{\frac{2}{3}}

512.5

Rewrite every power with base

2

Factor the smaller power from the numerator and denominator

Writing all terms as powers of

2,

\begin{aligned} \frac{8^{10}+4^{10}}{8^4+4^{11}} &=\frac{2^{30}+2^{20}}{2^{12}+2^{22}}\\ &=\frac{2^{20}(2^{10}+1)} {2^{12}(1+2^{10})}\\ &=2^8. \end{aligned}

Its positive square root is

2^4=16.

Thus the correct answer is B.

Problem 6 in other years