化简 243^{5/6}*3^{5/6}

解答

化简

24 3^{\frac{5}{6}} \cdot 3^{\frac{5}{6}}

243

求解步骤

24 3^{\frac{5}{6}} \cdot 3^{\frac{5}{6}}

使用指数法则:

a^{m} b^{m} = (ab)^{m}

24 3^{\frac{5}{6}} \cdot 3^{\frac{5}{6}} = (243 \cdot 3)^{\frac{5}{6}}

= (243 \cdot 3)^{\frac{5}{6}}

数字相乘:

243 \cdot 3 = 729

= 72 9^{\frac{5}{6}}

因式分解数字:

729 = 3^{6}

= (3^{6})^{\frac{5}{6}}

使用指数法则:

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

(3^{6})^{\frac{5}{6}} = 3^{6 \cdot \frac{5}{6}} = 3^{5}

= 3^{5}

整理后得

= 243

f a c t or x^{3} + 8 x^{2} + 15 x

f a c t or 81 a^{2} + 162 ab + 81 b^{2}

x + \frac{( 2 x )}{3} + \frac{( x )}{3} = 3600

s im pl i f y - \frac{9}{2} + 1

s im pl i f y \frac{1}{4 π ( 8.85 \cdot 1 0 ^{- 12} )}