vereinfachen (sqrt(x^2+y^2+z^2))^3

Lösung

vereinfachen

(x^{2} + y^{2} + z^{2})^{3}

(x^{2} + y^{2} + z^{2}) x^{2} + y^{2} + z^{2}

Schritte zur Lösung

(x^{2} + y^{2} + z^{2})^{3}

Wende Exponentenregel an:

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

(x^{2} + y^{2} + z^{2})^{2 + 1} = (x^{2} + y^{2} + z^{2})^{2} x^{2} + y^{2} + z^{2}

= (x^{2} + y^{2} + z^{2})^{2} x^{2} + y^{2} + z^{2}

Wende Exponentenregel an:

(n a)^{n} = a,

angenommen

n i s o dd or a \geq 0

(x^{2} + y^{2} + z^{2})^{2} = x^{2} + y^{2} + z^{2}

= (x^{2} + y^{2} + z^{2}) x^{2} + y^{2} + z^{2}

= x^{2} + y^{2} + z^{2} (x^{2} + y^{2} + z^{2})

= (x^{2} + y^{2} + z^{2}) x^{2} + y^{2} + z^{2}

s im pl i f y \frac{- 5}{- 2}

s im pl i f y 4 a^{2}

s im pl i f y (3 - 7) (3 - 7)

s im pl i f y 2^{x}

s im pl i f y - e^{- 3}