簡約 [(1/4)^2]^4

解

簡約

[(\frac{1}{4})^{2}]^{4}

\frac{1}{65536}

十進法表記

0.00001 \dots

解答ステップ

((\frac{1}{4})^{2})^{4}

指数の規則を適用する:

(a^{b})^{c} = a^{b c}, a \geq 0

= (\frac{1}{4})^{2 \cdot 4}

数を乗じる:

2 \cdot 4 = 8

= (\frac{1}{4})^{8}

指数の規則を適用する:

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

= \frac{1 ^{8}}{4 ^{8}}

1^{8} = 1

= \frac{1}{4 ^{8}}

4^{8} = 65536

= \frac{1}{65536}