Solve 1/2*3.3^3-5/2*3.3^2

$$\frac{ 1 }{ 2 } \times { 3.3 }^{ 3 } - \frac{ 5 }{ 2 } \times { 3.3 }^{ 2 }$$

Evaluate

$$-9.2565$$

Solution Steps

Calculate 3.3 to the power of 3 and get 35.937.

$$\frac{1}{2}\times 35.937-\frac{5}{2}\times 3.3^{2}$$

Convert decimal number 35.937 to fraction \frac{35937}{1000}.

$$\frac{1}{2}\times \frac{35937}{1000}-\frac{5}{2}\times 3.3^{2}$$

Multiply \frac{1}{2} times \frac{35937}{1000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 35937}{2\times 1000}-\frac{5}{2}\times 3.3^{2}$$

Do the multiplications in the fraction \frac{1\times 35937}{2\times 1000}.

$$\frac{35937}{2000}-\frac{5}{2}\times 3.3^{2}$$

Calculate 3.3 to the power of 2 and get 10.89.

$$\frac{35937}{2000}-\frac{5}{2}\times 10.89$$

Convert decimal number 10.89 to fraction \frac{1089}{100}.

$$\frac{35937}{2000}-\frac{5}{2}\times \frac{1089}{100}$$

Multiply \frac{5}{2} times \frac{1089}{100} by multiplying numerator times numerator and denominator times denominator.

$$\frac{35937}{2000}-\frac{5\times 1089}{2\times 100}$$

Do the multiplications in the fraction \frac{5\times 1089}{2\times 100}.

$$\frac{35937}{2000}-\frac{5445}{200}$$

Reduce the fraction \frac{5445}{200} to lowest terms by extracting and canceling out 5.

$$\frac{35937}{2000}-\frac{1089}{40}$$

Least common multiple of 2000 and 40 is 2000. Convert \frac{35937}{2000} and \frac{1089}{40} to fractions with denominator 2000.

$$\frac{35937}{2000}-\frac{54450}{2000}$$

Since \frac{35937}{2000} and \frac{54450}{2000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{35937-54450}{2000}$$

Subtract 54450 from 35937 to get -18513.

$$-\frac{18513}{2000}$$

Factor

$$-9.2565$$