Solve 13.593left(7+4.5*13.593-0.7/313.593^2right)

$$13.593 \left( 7+4.5 \cdot 13.593- \frac{ 0.7 }{ 3 } { 13.593 }^{ 2 } \right)$$

Evaluate

$$340.5805247667$$

Solution Steps

Multiply 4.5 and 13.593 to get 61.1685.

$$13.593\left(7+61.1685-\frac{0.7}{3}\times 13.593^{2}\right)$$

Add 7 and 61.1685 to get 68.1685.

$$13.593\left(68.1685-\frac{0.7}{3}\times 13.593^{2}\right)$$

Expand \frac{0.7}{3} by multiplying both numerator and the denominator by 10.

$$13.593\left(68.1685-\frac{7}{30}\times 13.593^{2}\right)$$

Calculate 13.593 to the power of 2 and get 184.769649.

$$13.593\left(68.1685-\frac{7}{30}\times 184.769649\right)$$

Convert decimal number 184.769649 to fraction \frac{184769649}{1000000}.

$$13.593\left(68.1685-\frac{7}{30}\times \frac{184769649}{1000000}\right)$$

Multiply \frac{7}{30} times \frac{184769649}{1000000} by multiplying numerator times numerator and denominator times denominator.

$$13.593\left(68.1685-\frac{7\times 184769649}{30\times 1000000}\right)$$

Do the multiplications in the fraction \frac{7\times 184769649}{30\times 1000000}.

$$13.593\left(68.1685-\frac{1293387543}{30000000}\right)$$

Reduce the fraction \frac{1293387543}{30000000} to lowest terms by extracting and canceling out 3.

$$13.593\left(68.1685-\frac{431129181}{10000000}\right)$$

Convert decimal number 68.1685 to fraction \frac{681685}{10000}. Reduce the fraction \frac{681685}{10000} to lowest terms by extracting and canceling out 5.

$$13.593\left(\frac{136337}{2000}-\frac{431129181}{10000000}\right)$$

Least common multiple of 2000 and 10000000 is 10000000. Convert \frac{136337}{2000} and \frac{431129181}{10000000} to fractions with denominator 10000000.

$$13.593\left(\frac{681685000}{10000000}-\frac{431129181}{10000000}\right)$$

Since \frac{681685000}{10000000} and \frac{431129181}{10000000} have the same denominator, subtract them by subtracting their numerators.

$$13.593\times \frac{681685000-431129181}{10000000}$$

Subtract 431129181 from 681685000 to get 250555819.

$$13.593\times \frac{250555819}{10000000}$$

Convert decimal number 13.593 to fraction \frac{13593}{1000}.

$$\frac{13593}{1000}\times \frac{250555819}{10000000}$$

Multiply \frac{13593}{1000} times \frac{250555819}{10000000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{13593\times 250555819}{1000\times 10000000}$$

Do the multiplications in the fraction \frac{13593\times 250555819}{1000\times 10000000}.

$$\frac{3405805247667}{10000000000}$$

Factor

$$\frac{3 \cdot 23 \cdot 197 \cdot 3253 \cdot 77023}{2 ^ {10} \cdot 5 ^ {10}} = 340\frac{5805247667}{10000000000} = 340.5805247667$$