展开 ((3!)/(2!1!))(9/16)^1(7/16)^2

解答

展开

(\frac{3 !}{2 ! 1 !}) (\frac{9}{16})^{1} (\frac{7}{16})^{2}

\frac{1323}{4096}

十进制

0.32299 \dots

求解步骤

(\frac{3 !}{2 ! \cdot 1 !}) (\frac{9}{16})^{1} (\frac{7}{16})^{2}

使用法则

a^{1} = a

(\frac{9}{16})^{1} = \frac{9}{16}

= (\frac{7}{16})^{2} \frac{9}{16} \cdot \frac{3 !}{2 ! \cdot 1 !}

\frac{3 !}{2 ! \cdot 1 !} = \frac{3}{1 !}

= (\frac{7}{16})^{2} \frac{3}{1 !} \cdot \frac{9}{16}

(\frac{7}{16})^{2} = \frac{7 ^{2}}{1 6 ^{2}}

= \frac{3}{1 !} \cdot \frac{9}{16} \cdot \frac{7 ^{2}}{1 6 ^{2}}

分式相乘:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{3 \cdot 9 \cdot 7 ^{2}}{1 ! \cdot 16 \cdot 1 6 ^{2}}

数字相乘:

3 \cdot 9 = 27

= \frac{7 ^{2} \cdot 27}{1 6 ^{2} \cdot 16 \cdot 1 !}

1! \cdot 16 \cdot 1 6^{2} = 1 6^{3} \cdot 1!

= \frac{7 ^{2} \cdot 27}{1 6 ^{3} \cdot 1 !}

27 \cdot 7^{2} = 1323

= \frac{1323}{1 6 ^{3} \cdot 1 !}

1! \cdot 1 6^{3} = 4096

= \frac{1323}{4096}

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