Solve 2.5^40-1/2.5-1

$$\frac{ { 2.5 }^{ 40 } -1 }{ 2.5-1 }$$

Evaluate

$$5514537417020183.832476057947133085690438747406005859375$$

Solution Steps

Calculate 2.5 to the power of 40 and get 8271806125530276.7487140869206996285356581211090087890625.

$$\frac{8271806125530276.7487140869206996285356581211090087890625-1}{2.5-1}$$

Subtract 1 from 8271806125530276.7487140869206996285356581211090087890625 to get 8271806125530275.7487140869206996285356581211090087890625.

$$\frac{8271806125530275.7487140869206996285356581211090087890625}{2.5-1}$$

Subtract 1 from 2.5 to get 1.5.

$$\frac{8271806125530275.7487140869206996285356581211090087890625}{1.5}$$

Expand \frac{8271806125530275.7487140869206996285356581211090087890625}{1.5} by multiplying both numerator and the denominator by 10000000000000000000000000000000000000000.

$$\frac{82718061255302757487140869206996285356581211090087890625}{15000000000000000000000000000000000000000}$$

Reduce the fraction \frac{82718061255302757487140869206996285356581211090087890625}{15000000000000000000000000000000000000000} to lowest terms by extracting and canceling out 27284841053187847137451171875.

$$\frac{3031649005909760426546254283}{549755813888}$$

Factor

$$\frac{7 \cdot 11 \cdot 29 \cdot 41 \cdot 61 \cdot 641 \cdot 1031 \cdot 3761 \cdot 5521 \cdot 39558401}{2 ^ {39}} = 5514537417020185$$