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If \(n\) and \(p\) are positive and \(2n^{9}p^{-1}=12n^{7}\), what is \(n^{-2}\) in terms of \(p\)?

(A) \(\ \ \sqrt{6p}\)

(B) \(\ \ 6p\)

(C) \(\ \ \frac{6}{p}\)

(D) \(\ \ \frac{1}{6p}\)

(E) \(\ \ \frac{1}{10p}\)

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If \(h=k^{6}\) for any positive integer \(k\), and \(y=h^{5}+h^{2}+h\), what is \(y\) in terms of \(k\)?

(A) \(\ \ k^{5}+k^{2}+k \)

(B) \(\ \ k^{6} \)

(C) \(\ \ k^{6}+k^{5}+k \)

(D) \(\ \ k^{11}+k^{8}+k^{6} \)

(E) \(\ \ k^{30}+k^{12}+k^{6} \)

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\(x,y,s,\) and \(t\) are positive numbers. If \( x^{\frac{27}{10}}=s^{3}\) and \(y^{\frac{-27}{10}}=t^{-3}\), what is \((xy)^{-\frac{9}{10}}\) in terms of \(s\) and \(t\)?

(A) \(\ \ 0\)

(B) \(\ \ \frac{1}{st}\)

(C) \(\ \ \frac{s}{t}\)

(D) \(\ \ \frac{t}{s}\)

(E) \(\ \ st\)

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If \(n\) is a positive integer and \(m=5 \cdot \clubsuit \cdot n^{5}\), where \( \clubsuit\) is the reciprocal of \(n\), what is \(m\) in terms of \(n\)?

(A) \(\ \ \frac{n^{4}}{5}\)

(B) \(\ \ 5n^{4}\)

(C) \(\ \ 5n^{5}\)

(D) \(\ \ n^{4}\)

(E) \(\ \ 5\cdot \clubsuit \cdot n^{4}\)

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If \(n\) is a positive integer and \( 9^{n}+9^{n+2}=k \), what is \( 9^{n+1} \) in terms of \(k\)?

(A) \(\ \ \frac{k-1}{9}\)

(B) \(\ \ \frac{k}{82}\)

(C) \(\ \ \frac{9k}{82}\)

(D) \(\ \ 9k\)

(E) \(\ \ 9k+9\)

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