Solve -1/8(1-{left(1/16right)}^10div1-1/16

$$- \frac{ 1 }{ 8 } (1- { \left( \frac{ 1 }{ 16 } \right) }^{ 10 } \div 1- \frac{ 1 }{ 16 }$$

Evaluate

$$-\frac{1030792151039}{8796093022208}\approx -0.1171875$$

Solution Steps

Calculate \frac{1}{16} to the power of 10 and get \frac{1}{1099511627776}.

$$-\frac{1}{8}\left(1-\frac{\frac{1}{1099511627776}}{1}-\frac{1}{16}\right)$$

Anything divided by one gives itself.

$$-\frac{1}{8}\left(1-\frac{1}{1099511627776}-\frac{1}{16}\right)$$

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

$$-\frac{1}{8}\left(\frac{1099511627776}{1099511627776}-\frac{1}{1099511627776}-\frac{1}{16}\right)$$

Since \frac{1099511627776}{1099511627776} and \frac{1}{1099511627776} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{8}\left(\frac{1099511627776-1}{1099511627776}-\frac{1}{16}\right)$$

Subtract 1 from 1099511627776 to get 1099511627775.

$$-\frac{1}{8}\left(\frac{1099511627775}{1099511627776}-\frac{1}{16}\right)$$

Least common multiple of 1099511627776 and 16 is 1099511627776. Convert \frac{1099511627775}{1099511627776} and \frac{1}{16} to fractions with denominator 1099511627776.

$$-\frac{1}{8}\left(\frac{1099511627775}{1099511627776}-\frac{68719476736}{1099511627776}\right)$$

Since \frac{1099511627775}{1099511627776} and \frac{68719476736}{1099511627776} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{8}\times \frac{1099511627775-68719476736}{1099511627776}$$

Subtract 68719476736 from 1099511627775 to get 1030792151039.

$$-\frac{1}{8}\times \frac{1030792151039}{1099511627776}$$

Multiply -\frac{1}{8} times \frac{1030792151039}{1099511627776} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-1030792151039}{8\times 1099511627776}$$

Do the multiplications in the fraction \frac{-1030792151039}{8\times 1099511627776}.

$$\frac{-1030792151039}{8796093022208}$$

Fraction \frac{-1030792151039}{8796093022208} can be rewritten as -\frac{1030792151039}{8796093022208} by extracting the negative sign.

$$-\frac{1030792151039}{8796093022208}$$

Factor

$$-\frac{1030792151039}{8796093022208} = -0.11718749999988631$$