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受欢迎的代数 >

化简 (8^{1/2})^3

解答

化简

(8^{\frac{1}{2}})^{3}

解答

16 \cdot 2^{\frac{1}{2}}

+1

十进制

22.62741 \dots

求解步骤

(8^{\frac{1}{2}})^{3}

使用指数法则:

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

= 8^{\frac{1}{2} \cdot 3}

\frac{1}{2} \cdot 3 = \frac{3}{2}

= 8^{\frac{3}{2}}

8

质因数分解:

2^{3}

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

使用指数法则:

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

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

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

使用指数法则:

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

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

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

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

= 8 \cdot 2^{\frac{3}{2}}

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

= 8 \cdot 2 \cdot 2^{\frac{1}{2}}

数字相乘:

8 \cdot 2 = 16

= 16 \cdot 2^{\frac{1}{2}}

流行的例子

化简 pi/2-pi/4

s im pl i f y \frac{π}{2} - \frac{π}{4}

-7(1-4m)=13(2m-3)

- 7 (1 - 4 m) = 13 (2 m - 3)

s im pl i f y 8 1^{2}

n^{2} + 2 n - 15 = 0

- (2 k - 11) = 7