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# SAT Change the Subject

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) $$\ \ \frac{1}{10p}$$

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) $$\ \ k^{30}+k^{12}+k^{6}$$

$$x,y,s,$$ 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) $$\ \ st$$

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) $$\ \ 5\cdot \clubsuit \cdot n^{4}$$

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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