vereinfachen \sqrt[5]{ab}*\sqrt[3]{a^2b^2}

Lösung

vereinfachen

5 ab \cdot 3 a^{2} b^{2}

a^{\frac{13}{15}} b^{\frac{13}{15}}

Schritte zur Lösung

5 ab 3 a^{2} b^{2}

Wende Radikal Regel an:

n ab = n a n b

5 ab = 5 a 5 b

= 5 a 5 b 3 a^{2} b^{2}

3 a^{2} b^{2} : a^{\frac{2}{3}} b^{\frac{2}{3}}

= 5 a 5 b a^{\frac{2}{3}} b^{\frac{2}{3}}

Wende Exponentenregel an:

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

5 a a^{\frac{2}{3}} = a^{\frac{1}{5}} a^{\frac{2}{3}} = a^{\frac{1}{5} + \frac{2}{3}}

= 5 b a^{\frac{1}{5} + \frac{2}{3}} b^{\frac{2}{3}}

Wende Exponentenregel an:

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

5 b b^{\frac{2}{3}} = b^{\frac{1}{5}} b^{\frac{2}{3}} = b^{\frac{1}{5} + \frac{2}{3}}

= a^{\frac{1}{5} + \frac{2}{3}} b^{\frac{1}{5} + \frac{2}{3}}

a^{\frac{1}{5} + \frac{2}{3}} = a^{\frac{13}{15}}

= a^{\frac{13}{15}} b^{\frac{1}{5} + \frac{2}{3}}

b^{\frac{1}{5} + \frac{2}{3}} = b^{\frac{13}{15}}

= a^{\frac{13}{15}} b^{\frac{13}{15}}

lo g_{3} (33) = x

- 5 x + 17 = 27

0.5 y = 19.5

(x - 1)^{2} + 11 x + 199 = 3 x^{2} - (x - 2)^{2}

y^{2} - 4 y = 21