簡約 5*15^3(3^{-8})^{1/2}

解

簡約

5 \cdot 1 5^{3} (3^{- 8})^{\frac{1}{2}}

\frac{625}{3}

十進法表記

208.33333 \dots

解答ステップ

5 \cdot 1 5^{3} (3^{- 8})^{\frac{1}{2}}

1 5^{3} = 3375

= 5 \cdot 3375 (3^{- 8})^{\frac{1}{2}}

指数の規則を適用する:

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

(3^{- 8})^{\frac{1}{2}} = 3^{- 8 \cdot \frac{1}{2}}

= 5 \cdot 3375 \cdot 3^{- 8 \cdot \frac{1}{2}}

- 8 \cdot \frac{1}{2} = - 4

= 5 \cdot 3375 \cdot 3^{- 4}

指数の規則を適用する:

a^{- b} = \frac{1}{a ^{b}}

3^{- 4} = \frac{1}{3 ^{4}}

= 5 \cdot 3375 \cdot \frac{1}{3 ^{4}}

3^{4} = 81

= 5 \cdot 3375 \cdot \frac{1}{81}

数を乗じる:

5 \cdot 3375 = 16875

= 16875 \cdot \frac{1}{81}

= \frac{1}{81} \cdot 16875

\frac{1}{81} \cdot 16875 = \frac{625}{3}

= \frac{625}{3}