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受欢迎的代数 >

化简 1000^{3/2}

解答

化简

100 0^{\frac{3}{2}}

解答

10000 \cdot 1 0^{\frac{1}{2}}

+1

十进制

31622.77660 \dots

求解步骤

100 0^{\frac{3}{2}}

1000

质因数分解:

2^{3} \cdot 5^{3}

= (2^{3} \cdot 5^{3})^{\frac{3}{2}}

使用指数法则:

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

2^{3} \cdot 5^{3} = 2^{2} \cdot 2 \cdot 5^{2} \cdot 5

= (2^{2} \cdot 2 \cdot 5^{2} \cdot 5)^{\frac{3}{2}}

= (2^{2} \cdot 5^{2} \cdot 2 \cdot 5)^{\frac{3}{2}}

使用指数法则:

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

(2^{2} \cdot 5^{2} \cdot 2 \cdot 5)^{\frac{3}{2}} = (2^{2})^{\frac{3}{2}} (5^{2})^{\frac{3}{2}} (2 \cdot 5)^{\frac{3}{2}}

= (2^{2})^{\frac{3}{2}} (5^{2})^{\frac{3}{2}} (2 \cdot 5)^{\frac{3}{2}}

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

= 8 (5^{2})^{\frac{3}{2}} (2 \cdot 5)^{\frac{3}{2}}

(5^{2})^{\frac{3}{2}} = 125

= 8 \cdot 125 (2 \cdot 5)^{\frac{3}{2}}

(2 \cdot 5)^{\frac{3}{2}} = 10 \cdot 1 0^{\frac{1}{2}}

= 8 \cdot 125 \cdot 10 \cdot 1 0^{\frac{1}{2}}

数字相乘:

8 \cdot 125 \cdot 10 = 10000

= 10000 \cdot 1 0^{\frac{1}{2}}

流行的例子

因式分解-5x^3-55x^2-150x

f a c t or - 5 x^{3} - 55 x^{2} - 150 x

因式分解 3ax-2by-2bx-6a+3ay+4b

f a c t or 3 a x - 2 b y - 2 b x - 6 a + 3 a y + 4 b

(-3x-3)/5 =3-4(x+2)

\frac{- 3 x - 3}{5} = 3 - 4 (x + 2)

0.2 x^{2} + 1.2 = 3.4

因式分解 3(x^2+10x+25)-4(x+5)

f a c t or 3 (x^{2} + 10 x + 25) - 4 (x + 5)