vereinfachen (5/2)^{10}((5/4)^5)^{-2}

Lösung

vereinfachen

(\frac{5}{2})^{10} ((\frac{5}{4})^{5})^{- 2}

1024

Schritte zur Lösung

(\frac{5}{2})^{10} ((\frac{5}{4})^{5})^{- 2}

(\frac{5}{2})^{10} = \frac{9765625}{1024}

= \frac{9765625}{1024} ((\frac{5}{4})^{5})^{- 2}

Wende Exponentenregel an:

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

((\frac{5}{4})^{5})^{- 2} = (\frac{5}{4})^{5 (- 2)}

= \frac{9765625}{1024} (\frac{5}{4})^{5 (- 2)}

5 (- 2) = - 10

= \frac{9765625}{1024} (\frac{5}{4})^{- 10}

Wende Exponentenregel an:

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

(\frac{5}{4})^{- 10} = \frac{1}{( \frac{5}{4} ) ^{10}}

= \frac{9765625}{1024} \cdot \frac{1}{( \frac{5}{4} ) ^{10}}

(\frac{5}{4})^{10} = \frac{9765625}{1048576}

= \frac{9765625}{1024} \cdot \frac{1}{\frac{9765625}{1048576}}

Wende Bruchregel an:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{9765625}{1024} \cdot \frac{1048576}{9765625}

kürze gemeinsame Faktoren über Kreuz:

9765625

= \frac{1048576}{1024}

Streiche

\frac{1048576}{1024} : 1024

= 1024

∣ 3 x - 6 ∣ + 9 = 12

6 x + 5 x = - 11

- 3 x + 6 \leq 12

∣ 2 x ∣ = 2 x^{2} + x - 4

s im pl i f y \frac{15}{20}