zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的代数 >

化简 \sqrt[5]{(2\sqrt[13]{4})^2}

解答

化简

5 (2134)^{2}

解答

2^{\frac{6}{13}}

+1

十进制

1.37700 \dots

求解步骤

5 (2134)^{2}

使用根式运算法则:

n a = a^{\frac{1}{n}}

= ((2134)^{2})^{\frac{1}{5}}

使用指数法则:

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

= (2134)^{2 \cdot \frac{1}{5}}

2 \cdot \frac{1}{5} = \frac{2}{5}

= (2134)^{\frac{2}{5}}

使用指数法则:

(a \cdot b)^{n} = a^{n} b^{n}

= 2^{\frac{2}{5}} (134)^{\frac{2}{5}}

(134)^{\frac{2}{5}} : 4^{\frac{2}{65}}

= 2^{\frac{2}{5}} \cdot 4^{\frac{2}{65}}

分解整数

4 = 2^{2}

= 2^{\frac{2}{5}} (2^{2})^{\frac{2}{65}}

使用指数法则:

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

(2^{2})^{\frac{2}{65}} = 2^{2 \cdot \frac{2}{65}}

= 2^{\frac{2}{5}} \cdot 2^{2 \cdot \frac{2}{65}}

整理后得

= 2^{\frac{2}{5}} \cdot 2^{\frac{4}{65}}

使用指数法则:

a^{b} \cdot a^{c} = a^{b + c}

2^{\frac{2}{5}} \cdot 2^{\frac{4}{65}} = 2^{\frac{2}{5} + \frac{4}{65}}

= 2^{\frac{2}{5} + \frac{4}{65}}

化简

\frac{2}{5} + \frac{4}{65} : \frac{6}{13}

= 2^{\frac{6}{13}}

流行的例子

化简 2ef^{-1}

s im pl i f y 2 e f^{- 1}

化简 sqrt(\sqrt[3]{512.64)}

s im pl i f y 3 512.64

化简 (\sqrt[4]{-16})^5

s im pl i f y (4 - 16)^{5}

合并 5sqrt(5)*xsqrt(x)

j o in 55 \cdot x x

化简 ((e^{-3x})+(e^{7x}))^{-11}

s im pl i f y ((e^{- 3 x}) + (e^{7 x}))^{- 11}