vereinfachen (1/2 x^{-1/2})^2

Lösung

vereinfachen

(\frac{1}{2} x^{- \frac{1}{2}})^{2}

\frac{1}{4 x}

Schritte zur Lösung

(\frac{1}{2} x^{- \frac{1}{2}})^{2}

Wende Exponentenregel an:

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

(\frac{1}{2} x^{- \frac{1}{2}})^{2} = (\frac{1}{2})^{2} (x^{- \frac{1}{2}})^{2}

= (\frac{1}{2})^{2} (x^{- \frac{1}{2}})^{2}

(\frac{1}{2})^{2} = \frac{1}{4}

= \frac{1}{4} (x^{- \frac{1}{2}})^{2}

Wende Exponentenregel an:

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

angenommen

a \geq 0

(x^{- \frac{1}{2}})^{2} = x^{- \frac{1}{2} \cdot 2}

= \frac{1}{4} x^{- \frac{1}{2} \cdot 2}

- \frac{1}{2} \cdot 2 = - 1

= \frac{1}{4} x^{- 1}

Wende Exponentenregel an:

a^{- 1} = \frac{1}{a}

x^{- 1} = \frac{1}{x}

= \frac{1}{4} \cdot \frac{1}{x}

Vereinfache

\frac{1}{4} \cdot \frac{1}{x} : \frac{1}{4 x}

= \frac{1}{4 x}

\frac{3}{4} x^{2} - \frac{1}{3} x + \frac{3}{2} = 0

∣ 10 - x ∣ > 5

8 x = 16

s im pl i f y \frac{1}{2 π \cdot 0.8761 \cdot 1 0 ^{3} \cdot 2.2 \cdot 1 0 ^{- 6}}

\frac{x - 1}{x + 5} > 2