簡約 (((-3/4)^2)^3)^2

解

簡約

((- \frac{3}{4})^{2})^{3}^{2}

\frac{531441}{16777216}

十進法表記

0.03167 \dots

解答ステップ

((- \frac{3}{4})^{2})^{3}^{2}

((- \frac{3}{4})^{2})^{3} : (- \frac{3}{4})^{6}

= ((- \frac{3}{4})^{6})^{2}

(- \frac{3}{4})^{6} = \frac{3 ^{6}}{4 ^{6}}

= (\frac{3 ^{6}}{4 ^{6}})^{2}

指数の規則を適用する:

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

= \frac{( 3 ^{6} ) ^{2}}{( 4 ^{6} ) ^{2}}

(4^{6})^{2} : 4^{12}

= \frac{( 3 ^{6} ) ^{2}}{4 ^{12}}

(3^{6})^{2} : 3^{12}

= \frac{3 ^{12}}{4 ^{12}}

3^{12} = 531441

= \frac{531441}{4 ^{12}}

4^{12} = 16777216

= \frac{531441}{16777216}