vereinfachen 32^{2/3}

Lösung

vereinfachen

3 2^{\frac{2}{3}}

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

Dezimale

10.07936 \dots

Schritte zur Lösung

3 2^{\frac{2}{3}}

Primfaktorzerlegung von

32 : 2^{5}

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

Wende Exponentenregel an:

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

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

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

Wende Exponentenregel an:

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

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

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

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

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

Wende Exponentenregel an:

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

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

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

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

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

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

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

Multipliziere die Zahlen:

4 \cdot 2 = 8

= 8 \cdot 2^{\frac{1}{3}}

s im pl i f y \frac{186000000 π}{8765.8 \cdot 4}

x^{2} - 4 x - 224 = 0

- \frac{1}{2} x - 7 = 18

f a c t or n^{2} - 30 n + 56

s im pl i f y - 3 (\frac{3}{2})^{0}