Solve 10241-0.5^7/1-0.5

$$1024 \frac{ 1- { 0.5 }^{ 7 } }{ 1-0.5 }$$

Evaluate

$$2032$$

Solution Steps

Calculate 0.5 to the power of 7 and get 0.0078125.

$$1024\times \frac{1-0.0078125}{1-0.5}$$

Subtract 0.0078125 from 1 to get 0.9921875.

$$1024\times \frac{0.9921875}{1-0.5}$$

Subtract 0.5 from 1 to get 0.5.

$$1024\times \frac{0.9921875}{0.5}$$

Expand \frac{0.9921875}{0.5} by multiplying both numerator and the denominator by 10000000.

$$1024\times \frac{9921875}{5000000}$$

Reduce the fraction \frac{9921875}{5000000} to lowest terms by extracting and canceling out 78125.

$$1024\times \frac{127}{64}$$

Express 1024\times \frac{127}{64} as a single fraction.

$$\frac{1024\times 127}{64}$$

Multiply 1024 and 127 to get 130048.

$$\frac{130048}{64}$$

Divide 130048 by 64 to get 2032.

$$2032$$

Factor

$$127\times 2^{4}$$