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受欢迎的代数 >

化简 256^{4/3}

解答

化简

25 6^{\frac{4}{3}}

解答

1024 \cdot 2^{\frac{2}{3}}

+1

十进制

1625.49867 \dots

求解步骤

25 6^{\frac{4}{3}}

256

质因数分解:

2^{8}

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

使用指数法则:

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

2^{8} = 2^{6} \cdot 2^{2}

= (2^{6} \cdot 2^{2})^{\frac{4}{3}}

使用指数法则:

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

(2^{6} \cdot 2^{2})^{\frac{4}{3}} = (2^{6})^{\frac{4}{3}} (2^{2})^{\frac{4}{3}}

= (2^{6})^{\frac{4}{3}} (2^{2})^{\frac{4}{3}}

(2^{6})^{\frac{4}{3}} = 256

= 256 (2^{2})^{\frac{4}{3}}

使用指数法则:

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

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

= 256 \cdot 2^{2 \cdot \frac{4}{3}}

2 \cdot \frac{4}{3} = \frac{8}{3}

= 256 \cdot 2^{\frac{8}{3}}

2^{\frac{8}{3}} = 4 \cdot 2^{\frac{2}{3}}

= 256 \cdot 4 \cdot 2^{\frac{2}{3}}

数字相乘:

256 \cdot 4 = 1024

= 1024 \cdot 2^{\frac{2}{3}}

流行的例子

- 8 + 4 \div 2 + 5

因式分解 xy-2x+4y-8

f a c t or x y - 2 x + 4 y - 8

3 x^{2} + 48 = 0

- 4 x = 7

因式分解 sqrt(64-k^2)

f a c t or 64 - k^{2}