化简 sqrt(\sqrt[3]{216*\sqrt{4)}}

解答

化简

3 216 \cdot 4

3 2^{2} 3

十进制

2.74945 \dots

求解步骤

32164

32164 = 632

= 632

使用根式运算法则:

ab = a b, a \geq 0, b \geq 0

632 = 632

= 632

32 = 62

= 662

分解整数

6 = 2 \cdot 3

= 2 \cdot 3 62

使用根式运算法则:

n ab = n a n b

2 \cdot 3 = 23

= 2362

使用指数法则:

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

262 = 2^{\frac{1}{2}} \cdot 2^{\frac{1}{6}} = 2^{\frac{1}{2} + \frac{1}{6}}

= 3 \cdot 2^{\frac{1}{2} + \frac{1}{6}}

2^{\frac{1}{2} + \frac{1}{6}} = 2^{\frac{2}{3}}

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

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

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

= 3 2^{2} 3

s im pl i f y a \cdot (e^{- (\frac{( x - b )}{c})})^{2}

e x p an d (x^{4} + 4)^{- \frac{1}{2}}

s im pl i f y - e^{- x} (x^{2} + 2 x + 2)

s im pl i f y (42) 2

s im pl i f y 12 2^{2}