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# SAT Exponents

If $$x, y,$$ and $$z$$ are positive numbers and $$M=\frac{7x^{6}y^{10}}{z^{6}}$$, what happens to $$M$$ when $$x$$ is halved, $$y$$ is doubled, and $$z$$ is tripled?

(A) it remains the same
(B) it gets multiplied by $$\frac{2}{3}$$
(C) it gets multiplied by $$\frac{7}{3}$$
(D) it gets multiplied by $$\frac{16}{729}$$
(E) it gets multiplied by $$\frac{65536}{729}$$

If $$k$$ is a positive integer, which of the following is equivalent to $$\left(13 \times 2^{-k-2} \right) - \left(6 \times 2^{-k-2} \right)?$$

(A) $$\ \ \frac{7}{4 \cdot 2^{k}}$$

(B) $$\ \ \frac{19}{4 \cdot 2^{k}}$$

(C) $$\ \ \frac{7 \cdot 2^{k}}{4}$$

(D) $$\ \ 28 \cdot 2^{k}$$

(E) $$\ \ 76 \cdot 2^{k}$$

Let $$x$$, $$y$$, and $$z$$ be positive numbers. If $$xyz=3$$, which of the following equals $$3 \cdot \frac{x^{3}}{y^{2}} \cdot \frac{z^{5}}{y^{-4}} \cdot \frac{1}{xz^{3}}$$?

(A) $$\ \ 1$$
(B) $$\ \ 3$$
(C) $$\ \ 9$$
(D) $$\ \ 27$$
(E) $$\ \ 3x^{2}z^{2}y^{-2}$$

If $$x$$ and $$y$$ are positive numbers and $$8^{3x} \cdot (64)^{3y}=4096$$, what is $$x+2y$$?

(A) $$\ \ \frac{3}{8}$$

(B) $$\ \ \frac{4}{3}$$

(C) $$\ \ 4$$

(D) $$\ \ 512$$

(E) $$\ \ 4096$$

If $$x$$ and $$y$$ are positive integers and $$6^{3x} \cdot 6^{3y} = 216$$ what is $$6x+6y$$?

(A) $$\ \ 0$$
(B) $$\ \ 1$$
(C) $$\ \ 3$$
(D) $$\ \ 6$$
(E) $$\ \ 216$$

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