Wie dividiere ich 0.5x1^-(1/2) durch x1^(1/2) korrekt?

Question

Aufgabe:

Im Titel.

Problem/Ansatz:

-0.5x1^-1 ?

Answer 1

= (0.5x^(-1/2)) / (x^(1/2))
= 0.5 (x^(-1/2)) / (x^(1/2))
= 0.5 (x^(-1/2 - 1/2))
= 0.5 x^(-1)
= 0.5/x

Comments

Und wenn es lauten würde: x^1/2 / 1/2* x^-1/2 ?

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Du meinst x^1/2  / ( 1/2 * x^-1/2 )?

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Ja, sorry war der Texteditor.

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= x^1/2  / ( 1/2 * x^-1/2 ) 
= 2 * x^1/2 / x^-1/2
= 2 * x^{1/2 - (-1/2)}
= 2 * x

Answer 2

a^(-1/2)/a^(1/2) = a^(-1/2 -1/2) = a^(-1) = 1/a

Answer 3

allgemein gilt:

a^m/a^n= a^(m-n)

=0.5 x₁^(-1/2 -1/2)

=0.5 x₁^(-1)

=0.5/x₁