The value of (116)^a^0+(116a)^0 -64^-(1)/(2)-(-32)^-(4)/(5) is:

1954 AMC 12 Problem 6

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The value of

\left(\dfrac1{16}\right)^{a^0}+\left(\dfrac1{16a}\right)^0

{}-64^{-\frac{1}{2}}-(-32)^{-\frac{4}{5}}

is:

1\dfrac{13}{16}

1\dfrac3{16}

1

\dfrac78

\dfrac1{16}

Evaluate each of the four terms separately, using

a^0=1

The real fifth root of

-32

-2

, so

(-32)^{-\frac{4}{5}}=\frac{1}{16}

For permissible

a,

the four terms are

\frac1{16},\qquad 1,\qquad \frac18,\qquad \frac1{16}.

Therefore the expression is

\frac1{16}+1-\frac18-\frac1{16}=\frac78.

Thus, the correct answer is D.