簡約 \sqrt[4]{(3/2)}^8

解

簡約

4 (\frac{3}{2})^{8}

\frac{9}{4}

十進法表記

2.25

解答ステップ

(4 \frac{3}{2})^{8}

規則を適用する:

(a) = a

(\frac{3}{2}) = \frac{3}{2}

= (4 \frac{3}{2})^{8}

8

を書き換え

4 \cdot 2

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

指数の規則を適用する:

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

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

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

指数の規則を適用する:

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

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

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

指数の規則を適用する:

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

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

3^{2} = 9

= \frac{9}{2 ^{2}}

2^{2} = 4

= \frac{9}{4}