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受欢迎的代数 >

化简 \sqrt[4]{8}*\sqrt[3]{32}

解答

化简

48 \cdot 332

解答

4 12 2^{5}

+1

十进制

5.33935 \dots

求解步骤

48332

332 = 234

= 48 \cdot 234

分解整数

8 = 2^{3}

= 4 2^{3} \cdot 234

使用指数法则:

(a^{b})^{c} = a^{b c}

4 2^{3} = 2^{3 \cdot \frac{1}{4}}

= 2^{3 \cdot \frac{1}{4}} \cdot 234

整理后得

= 2^{\frac{3}{4}} \cdot 234

分解整数

4 = 2^{2}

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

使用指数法则:

(a^{b})^{c} = a^{b c}

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

= 2^{\frac{3}{4}} \cdot 2 \cdot 2^{2 \cdot \frac{1}{3}}

整理后得

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

使用指数法则:

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

2^{\frac{3}{4}} \cdot 2 \cdot 2^{\frac{2}{3}} = 2^{\frac{3}{4} + 1 + \frac{2}{3}}

= 2^{\frac{3}{4} + 1 + \frac{2}{3}}

化简

\frac{3}{4} + 1 + \frac{2}{3} : \frac{29}{12}

= 2^{\frac{29}{12}}

2^{\frac{29}{12}} = 2^{2 + \frac{5}{12}}

= 2^{2 + \frac{5}{12}}

使用指数法则:

x^{a + b} = x^{a} x^{b}

= 2^{2} \cdot 2^{\frac{5}{12}}

2^{2} = 4

= 4 \cdot 2^{\frac{5}{12}}

= 2^{\frac{5}{12}} \cdot 4

2^{\frac{5}{12}} = 12 2^{5}

= 12 2^{5} \cdot 4

= 4 12 2^{5}

流行的例子

2x^3-x^2-41x-20>= 0

2 x^{3} - x^{2} - 41 x - 20 \geq 0

因式分解 8x^2+32x+x+4

f a c t or 8 x^{2} + 32 x + x + 4

因式分解-81r^2+1

f a c t or - 81 r^{2} + 1

5 x - \frac{1}{4} = \frac{8}{2}

(x - 4) (x - 10) = - 9