簡約 (((((12))/((23)^2))^2)^2)^2

解

簡約

(\frac{( 12 )}{( 23 ) ^{2}})^{2}^{2}^{2}

\frac{429981696}{2 3 ^{16}}

十進法表記

7.0114 E - 14

解答ステップ

(\frac{( 12 )}{( 23 ) ^{2}})^{2}^{2}^{2}

((\frac{12}{2 3 ^{2}})^{2})^{2} : (\frac{12}{2 3 ^{2}})^{4}

= ((\frac{12}{2 3 ^{2}})^{4})^{2}

指数の規則を適用する:

(a^{b})^{c} = a^{b c}

= (\frac{12}{2 3 ^{2}})^{4 \cdot 2}

数を乗じる:

4 \cdot 2 = 8

= (\frac{12}{2 3 ^{2}})^{8}

指数の規則を適用する:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{1 2 ^{8}}{( 2 3 ^{2} ) ^{8}}

(2 3^{2})^{8} : 2 3^{16}

= \frac{1 2 ^{8}}{2 3 ^{16}}

1 2^{8} = 429981696

= \frac{429981696}{2 3 ^{16}}