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4. 已知$10^{x}=5$. 求$10^{1-x}$的值.
答案
4. 2
5. 已知$x^{m}=-3$，$x^{n}=4$. 求$x^{3m-2n}$的值.
答案
5. $-\frac{27}{16}$
6. 已知$3^{m}=6$，$9^{n}=2$. 求$3^{2m-4n+1}$的值.
答案
6. 27
7. 已知$5^{a}=4$，$5^{b}=6$，$5^{c}=9$.
(1)求$5^{2a+b}$的值.
(2)求$5^{b-2c}$的值.
(3)试说明$2b=a+c$.
(1)求$5^{2a+b}$的值.
(2)求$5^{b-2c}$的值.
(3)试说明$2b=a+c$.
答案
解：(1)$5^{2a+b}=(5^{a})^{2}×5^{b}=4^{2}×6=96.$
(2)$5^{b-2c}=5^{b}÷(5^{c})^{2}=6÷9^{2}=\frac{2}{27}.$
(3)理由：因为 $5^{2b}=(5^{b})^{2}=6^{2}=36$,
$5^{a+c}=5^{a}×5^{c}=4×9=36$，所以$2b=a+c.$
(2)$5^{b-2c}=5^{b}÷(5^{c})^{2}=6÷9^{2}=\frac{2}{27}.$
(3)理由：因为 $5^{2b}=(5^{b})^{2}=6^{2}=36$,
$5^{a+c}=5^{a}×5^{c}=4×9=36$，所以$2b=a+c.$
