Solve -8.314*450*(-2.04-1176/450+2.1*10^7(1/450)^3)

$$- 8.314 \times 450 \times ( - 2.04 - \frac { 1176 } { 450 } + 2.1 \times 10 ^ { 7 } ( \frac { 1 } { 450 } ) ^ { 3 } )$$

Evaluate

$$\frac{111694433}{6750}\approx 16547.323407407$$

Solution Steps

Multiply -8.314 and 450 to get -3741.3.

$$-3741.3\left(-2.04-\frac{1176}{450}+2.1\times 10^{7}\times \left(\frac{1}{450}\right)^{3}\right)$$

Reduce the fraction \frac{1176}{450} to lowest terms by extracting and canceling out 6.

$$-3741.3\left(-2.04-\frac{196}{75}+2.1\times 10^{7}\times \left(\frac{1}{450}\right)^{3}\right)$$

Convert decimal number -2.04 to fraction -\frac{204}{100}. Reduce the fraction -\frac{204}{100} to lowest terms by extracting and canceling out 4.

$$-3741.3\left(-\frac{51}{25}-\frac{196}{75}+2.1\times 10^{7}\times \left(\frac{1}{450}\right)^{3}\right)$$

Least common multiple of 25 and 75 is 75. Convert -\frac{51}{25} and \frac{196}{75} to fractions with denominator 75.

$$-3741.3\left(-\frac{153}{75}-\frac{196}{75}+2.1\times 10^{7}\times \left(\frac{1}{450}\right)^{3}\right)$$

Since -\frac{153}{75} and \frac{196}{75} have the same denominator, subtract them by subtracting their numerators.

$$-3741.3\left(\frac{-153-196}{75}+2.1\times 10^{7}\times \left(\frac{1}{450}\right)^{3}\right)$$

Subtract 196 from -153 to get -349.

$$-3741.3\left(-\frac{349}{75}+2.1\times 10^{7}\times \left(\frac{1}{450}\right)^{3}\right)$$

Calculate 10 to the power of 7 and get 10000000.

$$-3741.3\left(-\frac{349}{75}+2.1\times 10000000\times \left(\frac{1}{450}\right)^{3}\right)$$

Multiply 2.1 and 10000000 to get 21000000.

$$-3741.3\left(-\frac{349}{75}[phone]\times \left(\frac{1}{450}\right)^{3}\right)$$

Calculate \frac{1}{450} to the power of 3 and get \frac{1}{91125000}.

$$-3741.3\left(-\frac{349}{75}[phone]\times \frac{1}{91125000}\right)$$

Multiply 21000000 and \frac{1}{91125000} to get \frac{21000000}{91125000}.

$$-3741.3\left(-\frac{349}{75}+\frac{21000000}{91125000}\right)$$

Reduce the fraction \frac{21000000}{91125000} to lowest terms by extracting and canceling out 375000.

$$-3741.3\left(-\frac{349}{75}+\frac{56}{243}\right)$$

Least common multiple of 75 and 243 is 6075. Convert -\frac{349}{75} and \frac{56}{243} to fractions with denominator 6075.

$$-3741.3\left(-\frac{28269}{6075}+\frac{1400}{6075}\right)$$

Since -\frac{28269}{6075} and \frac{1400}{6075} have the same denominator, add them by adding their numerators.

$$-3741.3\times \frac{-28269+1400}{6075}$$

Add -28269 and 1400 to get -26869.

$$-3741.3\left(-\frac{26869}{6075}\right)$$

Convert decimal number -3741.3 to fraction -\frac{37413}{10}.

$$-\frac{37413}{10}\left(-\frac{26869}{6075}\right)$$

Multiply -\frac{37413}{10} times -\frac{26869}{6075} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-37413\left(-26869\right)}{10\times 6075}$$

Do the multiplications in the fraction \frac{-37413\left(-26869\right)}{10\times 6075}.

$$\frac{1005249897}{60750}$$

Reduce the fraction \frac{1005249897}{60750} to lowest terms by extracting and canceling out 9.

$$\frac{111694433}{6750}$$

Factor

$$\frac{97 \cdot 277 \cdot 4157}{2 \cdot 3 ^ {3} \cdot 5 ^ {3}} = 16547\frac{2183}{6750} = 16547.323407407406$$