簡約 \sqrt[5]{(4/2)}^{10}

解

簡約

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

4

解答ステップ

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

規則を適用する:

(a) = a

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

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

10

を書き換え

5 \cdot 2

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

指数の規則を適用する:

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

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

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

指数の規則を適用する:

(n a)^{n} = a, n i s o dd or a \geq 0

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

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

指数の規則を適用する:

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

= \frac{4 ^{2}}{2 ^{2}}

4^{2} = 16

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

2^{2} = 4

= \frac{16}{4}

数を割る:

\frac{16}{4} = 4

= 4