Solve {left(87/256right)}^5+261/256-1

$${ \left( \frac{ 87 }{ 256 } \right) }^{ 5 } + \frac{ 261 }{ 256 } -1$$

Evaluate

$$\frac{26459045687}{1099511627776}=0.024064362$$

Solution Steps

Calculate \frac{87}{256} to the power of 5 and get \frac{4984209207}{1099511627776}.

$$\frac{4984209207}{1099511627776}+\frac{261}{256}-1$$

Least common multiple of 1099511627776 and 256 is 1099511627776. Convert \frac{4984209207}{1099511627776} and \frac{261}{256} to fractions with denominator 1099511627776.

$$\frac{4984209207}{1099511627776}+\frac{1120986464256}{1099511627776}-1$$

Since \frac{4984209207}{1099511627776} and \frac{1120986464256}{1099511627776} have the same denominator, add them by adding their numerators.

$$\frac{4984209207+1120986464256}{1099511627776}-1$$

Add 4984209207 and 1120986464256 to get 1125970673463.

$$\frac{1125970673463}{1099511627776}-1$$

Convert 1 to fraction \frac{1099511627776}{1099511627776}.

$$\frac{1125970673463}{1099511627776}-\frac{1099511627776}{1099511627776}$$

Since \frac{1125970673463}{1099511627776} and \frac{1099511627776}{1099511627776} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1125970673463-1099511627776}{1099511627776}$$

Subtract 1099511627776 from 1125970673463 to get 26459045687.

$$\frac{26459045687}{1099511627776}$$

Factor

$$\frac{26459045687}{2 ^ {40}} = 0.024064361866294348$$