Solve 1-41.9^3/14^3

$$1- \frac{ 4 { 1.9 }^{ 3 } }{ { 14 }^{ 3 } }$$

Evaluate

$$\frac{679141}{686000}\approx 0.990001458$$

Solution Steps

Calculate 1.9 to the power of 3 and get 6.859.

$$1-\frac{4\times 6.859}{14^{3}}$$

Multiply 4 and 6.859 to get 27.436.

$$1-\frac{27.436}{14^{3}}$$

Calculate 14 to the power of 3 and get 2744.

$$1-\frac{27.436}{2744}$$

Expand \frac{27.436}{2744} by multiplying both numerator and the denominator by 1000.

$$1-\frac{27436}{2744000}$$

Reduce the fraction \frac{27436}{2744000} to lowest terms by extracting and canceling out 4.

$$1-\frac{6859}{686000}$$

Convert 1 to fraction \frac{686000}{686000}.

$$\frac{686000}{686000}-\frac{6859}{686000}$$

Since \frac{686000}{686000} and \frac{6859}{686000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{686000-6859}{686000}$$

Subtract 6859 from 686000 to get 679141.

$$\frac{679141}{686000}$$

Factor

$$\frac{739 \cdot 919}{2 ^ {4} \cdot 5 ^ {3} \cdot 7 ^ {3}} = 0.9900014577259475$$