簡約 ([ 9/4 (9/4)^5]^2)/([(9/4)^2 9/4 ]^2)

解

簡約

\frac{[ \frac{9}{4} ( \frac{9}{4} ) ^{5} ] ^{2}}{[ ( \frac{9}{4} ) ^{2} \frac{9}{4} ] ^{2}}

\frac{531441}{4096}

十進法表記

129.74633 \dots

解答ステップ

\frac{( \frac{9}{4} ( \frac{9}{4} ) ^{5} ) ^{2}}{( ( \frac{9}{4} ) ^{2} \frac{9}{4} ) ^{2}}

交換法則を適用する:

(\frac{9}{4})^{2} \frac{9}{4} = \frac{9}{4} (\frac{9}{4})^{2}

= \frac{( \frac{9}{4} ( \frac{9}{4} ) ^{5} ) ^{2}}{( \frac{9}{4} ( \frac{9}{4} ) ^{2} ) ^{2}}

(\frac{9}{4} (\frac{9}{4})^{5})^{2} = (\frac{9}{4})^{2} \frac{9 ^{10}}{4 ^{10}}

= \frac{( \frac{9}{4} ) ^{2} \frac{9 ^{10}}{4 ^{10}}}{( \frac{9}{4} ( \frac{9}{4} ) ^{2} ) ^{2}}

(\frac{9}{4} (\frac{9}{4})^{2})^{2} = (\frac{9}{4})^{2} \frac{6561}{256}

= \frac{( \frac{9}{4} ) ^{2} \frac{9 ^{10}}{4 ^{10}}}{( \frac{9}{4} ) ^{2} \frac{6561}{256}}

共通因数を約分する:

(\frac{9}{4})^{2}

= \frac{\frac{9 ^{10}}{4 ^{10}}}{\frac{6561}{256}}

\frac{\frac{9 ^{10}}{4 ^{10}}}{\frac{6561}{256}} = \frac{531441}{4096}

= \frac{531441}{4096}