1990 AMC 12 Problem 2

Attempt Problem 2 of the 1990 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 1990 AMC 12 solutions, or check the answer key.

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\left(\dfrac14\right)^{-\frac{1}{4}}=

-16

-\sqrt2

-\frac1{16}

\frac1{256}

\sqrt2

A negative exponent takes the reciprocal

Rewrite

4

as a power of

2

Taking the reciprocal gives

4^{\frac{1}{4}}=(2^2)^{\frac{1}{4}}=2^{\frac{1}{2}}=\sqrt2.

Thus the correct answer is E.

Problem 2 in other years