Solve {left(1-25^4/6^2right)}^100

$${ \left(1-2 \frac{ { 5 }^{ 4 } }{ { 6 }^{ 2 } } \right) }^{ 100 }$$

Evaluate

$$\frac{208386273084501649591606462070057272458431606973479302911257080995361779466546944332681138471693514003886280864945113589278896573474881279906412638369038153041596183276279531741699116387542816670510478954563375656596524517452472816944462099792090278231266465753931953337674640001}{336705732427516898587460627772004697542605295316077247452351004740460372771448563031143507354757009822674618697405379563749376}\approx 6.18897313 \cdot 10^{152}$$

Solution Steps

Calculate 5 to the power of 4 and get 625.

$$\left(1-2\times \frac{625}{6^{2}}\right)^{100}$$

Calculate 6 to the power of 2 and get 36.

$$\left(1-2\times \frac{625}{36}\right)^{100}$$

Multiply 2 and \frac{625}{36} to get \frac{625}{18}.

$$\left(1-\frac{625}{18}\right)^{100}$$

Subtract \frac{625}{18} from 1 to get -\frac{607}{18}.

$$\left(-\frac{607}{18}\right)^{100}$$

Calculate -\frac{607}{18} to the power of 100 and get \frac{208386273084501649591606462070057272458431606973479302911257080995361779466546944332681138471693514003886280864945113589278896573474881279906412638369038153041596183276279531741699116387542816670510478954563375656596524517452472816944462099792090278231266465753931953337674640001}{336705732427516898587460627772004697542605295316077247452351004740460372771448563031143507354757009822674618697405379563749376}.

$$\frac{208386273084501649591606462070057272458431606973479302911257080995361779466546944332681138471693514003886280864945113589278896573474881279906412638369038153041596183276279531741699116387542816670510478954563375656596524517452472816944462099792090278231266465753931953337674640001}{336705732427516898587460627772004697542605295316077247452351004740460372771448563031143507354757009822674618697405379563749376}$$

Factor

$$\frac{607 ^ {100}}{2 ^ {100} \cdot 3 ^ {200}} = 6.188973130398403 \times 10^{152}\frac{3.2712237402199937 \times 10^{125}}{3.3670573242751693 \times 10^{125}} = 6.188973130398403 \times 10^{152}$$