化简 (27*64)^{2/3}

解答

化简

(27 \cdot 64)^{\frac{2}{3}}

144

求解步骤

(27 \cdot 64)^{\frac{2}{3}}

使用指数法则:

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

(27 \cdot 64)^{\frac{2}{3}} = 2 7^{\frac{2}{3}} \cdot 6 4^{\frac{2}{3}}

= 2 7^{\frac{2}{3}} \cdot 6 4^{\frac{2}{3}}

2 7^{\frac{2}{3}} = 9

= 9 \cdot 6 4^{\frac{2}{3}}

因式分解数字:

64 = 4^{3}

= 9 (4^{3})^{\frac{2}{3}}

使用指数法则:

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

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

= 9 \cdot 4^{3 \cdot \frac{2}{3}}

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

= 9 \cdot 4^{2}

4^{2} = 16

= 9 \cdot 16

数字相乘:

9 \cdot 16 = 144

= 144

(14 + 2 x) (26 + 2 x) = 1408

f a c t or x^{3} + 3 x^{2} y + 3 x y^{2} + y^{3}

3 d^{2} + d = - 2 d

- 1 < 2 x - 5 < 7

s im pl i f y (0.5 a - 0.6 b + 5.5) - (- 0.5 a + 0.4 b) + (1.3 b - 4.5)