vereinfachen 200(((\frac{1+0.07)/(12))^{12*35}-1}{(0.07)/(12)})

Lösung

vereinfachen

200 (\frac{( \frac{1 + 0.07}{12} ) ^{12 \cdot 35} - 1}{\frac{0.07}{12}})

\frac{25 ( 1.0 7 ^{420} - 1 2 ^{420} )}{0.07 \cdot 2 ^{835} \cdot 3 ^{419}}

Schritte zur Lösung

200 (\frac{( \frac{1 + 0.07}{12} ) ^{12 \cdot 35} - 1}{\frac{0.07}{12}})

Apply rule:

(a) = a

(\frac{( \frac{1 + 0.07}{12} ) ^{12 \cdot 35} - 1}{\frac{0.07}{12}}) = \frac{( \frac{1 + 0.07}{12} ) ^{12 \cdot 35} - 1}{\frac{0.07}{12}}

= 200 \cdot \frac{( \frac{1 + 0.07}{12} ) ^{12 \cdot 35} - 1}{\frac{0.07}{12}}

Wende Bruchregel an:

\frac{a}{\frac{b}{c}} = \frac{a \cdot c}{b}

\frac{( \frac{1 + 0.07}{12} ) ^{12 \cdot 35} - 1}{\frac{0.07}{12}} = \frac{( ( \frac{1 + 0.07}{12} ) ^{12 \cdot 35} - 1 ) \cdot 12}{0.07}

= 200 \cdot \frac{( ( \frac{1 + 0.07}{12} ) ^{12 \cdot 35} - 1 ) \cdot 12}{0.07}

Vereinfache

((\frac{1 + 0.07}{12})^{12 \cdot 35} - 1) \cdot 12 : \frac{1.0 7 ^{420} - 1 2 ^{420}}{1 2 ^{419}}

= 200 \cdot \frac{\frac{1.0 7 ^{420} - 1 2 ^{420}}{1 2 ^{419}}}{0.07}

Wende Bruchregel an:

\frac{\frac{a}{b}}{c} = \frac{a}{b \cdot c}

\frac{\frac{1.0 7 ^{420} - 1 2 ^{420}}{1 2 ^{419}}}{0.07} = \frac{1.0 7 ^{420} - 1 2 ^{420}}{1 2 ^{419} \cdot 0.07}

= 200 \cdot \frac{1.0 7 ^{420} - 1 2 ^{420}}{1 2 ^{419} \cdot 0.07}

200 \cdot \frac{1.0 7 ^{420} - 1 2 ^{420}}{1 2 ^{419} \cdot 0.07} = \frac{25 ( 1.0 7 ^{420} - 1 2 ^{420} )}{0.07 \cdot 2 ^{835} \cdot 3 ^{419}}

= \frac{25 ( 1.0 7 ^{420} - 1 2 ^{420} )}{0.07 \cdot 2 ^{835} \cdot 3 ^{419}}

x^{2} - 12 x - 1 = 0

0 = x^{2} + 2 x

- 44 > - 2 x - 8 \geq - 8

9 e + 4 = 5 e + 14 + 13 e

x + 4 = 13