Solve 256(1-0.5^6/1-0.5)

$$256( \frac{ 1- { 0.5 }^{ 6 } }{ 1-0.5 } )$$

Evaluate

$$504$$

Solution Steps

Calculate 0.5 to the power of 6 and get 0.015625.

$$256\times \frac{1-0.015625}{1-0.5}$$

Subtract 0.015625 from 1 to get 0.984375.

$$256\times \frac{0.984375}{1-0.5}$$

Subtract 0.5 from 1 to get 0.5.

$$256\times \frac{0.984375}{0.5}$$

Expand \frac{0.984375}{0.5} by multiplying both numerator and the denominator by 1000000.

$$256\times \frac{984375}{500000}$$

Reduce the fraction \frac{984375}{500000} to lowest terms by extracting and canceling out 15625.

$$256\times \frac{63}{32}$$

Express 256\times \frac{63}{32} as a single fraction.

$$\frac{256\times 63}{32}$$

Multiply 256 and 63 to get 16128.

$$\frac{16128}{32}$$

Divide 16128 by 32 to get 504.

$$504$$

Factor

$$7\times 2^{3}\times 3^{2}$$