Solve {left(43/128right)}^5+129/128-1

$${ \left( \frac{ 43 }{ 128 } \right) }^{ 5 } + \frac{ 129 }{ 128 } -1$$

Evaluate

$$\frac{415443899}{34359738368}=0.012091009$$

Solution Steps

Calculate \frac{43}{128} to the power of 5 and get \frac{147008443}{34359738368}.

$$\frac{147008443}{34359738368}+\frac{129}{128}-1$$

Least common multiple of 34359738368 and 128 is 34359738368. Convert \frac{147008443}{34359738368} and \frac{129}{128} to fractions with denominator 34359738368.

$$\frac{147008443}{34359738368}+\frac{34628173824}{34359738368}-1$$

Since \frac{147008443}{34359738368} and \frac{34628173824}{34359738368} have the same denominator, add them by adding their numerators.

$$\frac{147008443+34628173824}{34359738368}-1$$

Add 147008443 and 34628173824 to get 34775182267.

$$\frac{34775182267}{34359738368}-1$$

Convert 1 to fraction \frac{34359738368}{34359738368}.

$$\frac{34775182267}{34359738368}-\frac{34359738368}{34359738368}$$

Since \frac{34775182267}{34359738368} and \frac{34359738368}{34359738368} have the same denominator, subtract them by subtracting their numerators.

$$\frac{34775182267-34359738368}{34359738368}$$

Subtract 34359738368 from 34775182267 to get 415443899.

$$\frac{415443899}{34359738368}$$

Factor

$$\frac{13 \cdot 31957223}{2 ^ {35}} = 0.0120910088007804$$