Solve (-0.5*10^3+51/4*10^2-105*10-3)-(-0.5*7^3+51/47^2-105*7-3)

$$(-0.5 \times { 10 }^{ 3 } + \frac{ 51 }{ 4 } \times { 10 }^{ 2 } -105 \times 10-3)-(-0.5 \times { 7 }^{ 3 } + \frac{ 51 }{ 4 } { 7 }^{ 2 } -105 \times 7-3)$$

Evaluate

$$6.75$$

Solution Steps

Calculate 10 to the power of 3 and get 1000.

$$-0.5\times 1000+\frac{51}{4}\times 10^{2}-105\times 10-3-\left(-0.5\times 7^{3}+\frac{51}{4}\times 7^{2}-105\times 7-3\right)$$

Multiply -0.5 and 1000 to get -500.

$$-500+\frac{51}{4}\times 10^{2}-105\times 10-3-\left(-0.5\times 7^{3}+\frac{51}{4}\times 7^{2}-105\times 7-3\right)$$

Calculate 10 to the power of 2 and get 100.

$$-500+\frac{51}{4}\times 100-105\times 10-3-\left(-0.5\times 7^{3}+\frac{51}{4}\times 7^{2}-105\times 7-3\right)$$

Express \frac{51}{4}\times 100 as a single fraction.

$$-500+\frac{51\times 100}{4}-105\times 10-3-\left(-0.5\times 7^{3}+\frac{51}{4}\times 7^{2}-105\times 7-3\right)$$

Multiply 51 and 100 to get 5100.

$$-500+\frac{5100}{4}-105\times 10-3-\left(-0.5\times 7^{3}+\frac{51}{4}\times 7^{2}-105\times 7-3\right)$$

Divide 5100 by 4 to get 1275.

$$-500+1275-105\times 10-3-\left(-0.5\times 7^{3}+\frac{51}{4}\times 7^{2}-105\times 7-3\right)$$

Add -500 and 1275 to get 775.

$$775-105\times 10-3-\left(-0.5\times 7^{3}+\frac{51}{4}\times 7^{2}-105\times 7-3\right)$$

Multiply 105 and 10 to get 1050.

$$775-1050-3-\left(-0.5\times 7^{3}+\frac{51}{4}\times 7^{2}-105\times 7-3\right)$$

Subtract 1050 from 775 to get -275.

$$-275-3-\left(-0.5\times 7^{3}+\frac{51}{4}\times 7^{2}-105\times 7-3\right)$$

Subtract 3 from -275 to get -278.

$$-278-\left(-0.5\times 7^{3}+\frac{51}{4}\times 7^{2}-105\times 7-3\right)$$

Calculate 7 to the power of 3 and get 343.

$$-278-\left(-0.5\times 343+\frac{51}{4}\times 7^{2}-105\times 7-3\right)$$

Multiply -0.5 and 343 to get -171.5.

$$-278-\left(-171.5+\frac{51}{4}\times 7^{2}-105\times 7-3\right)$$

Calculate 7 to the power of 2 and get 49.

$$-278-\left(-171.5+\frac{51}{4}\times 49-105\times 7-3\right)$$

Express \frac{51}{4}\times 49 as a single fraction.

$$-278-\left(-171.5+\frac{51\times 49}{4}-105\times 7-3\right)$$

Multiply 51 and 49 to get 2499.

$$-278-\left(-171.5+\frac{2499}{4}-105\times 7-3\right)$$

Convert decimal number -171.5 to fraction -\frac{1715}{10}. Reduce the fraction -\frac{1715}{10} to lowest terms by extracting and canceling out 5.

$$-278-\left(-\frac{343}{2}+\frac{2499}{4}-105\times 7-3\right)$$

Least common multiple of 2 and 4 is 4. Convert -\frac{343}{2} and \frac{2499}{4} to fractions with denominator 4.

$$-278-\left(-\frac{686}{4}+\frac{2499}{4}-105\times 7-3\right)$$

Since -\frac{686}{4} and \frac{2499}{4} have the same denominator, add them by adding their numerators.

$$-278-\left(\frac{-686+2499}{4}-105\times 7-3\right)$$

Add -686 and 2499 to get 1813.

$$-278-\left(\frac{1813}{4}-105\times 7-3\right)$$

Multiply 105 and 7 to get 735.

$$-278-\left(\frac{1813}{4}-735-3\right)$$

Convert 735 to fraction \frac{2940}{4}.

$$-278-\left(\frac{1813}{4}-\frac{2940}{4}-3\right)$$

Since \frac{1813}{4} and \frac{2940}{4} have the same denominator, subtract them by subtracting their numerators.

$$-278-\left(\frac{1813-2940}{4}-3\right)$$

Subtract 2940 from 1813 to get -1127.

$$-278-\left(-\frac{1127}{4}-3\right)$$

Convert 3 to fraction \frac{12}{4}.

$$-278-\left(-\frac{1127}{4}-\frac{12}{4}\right)$$

Since -\frac{1127}{4} and \frac{12}{4} have the same denominator, subtract them by subtracting their numerators.

$$-278-\frac{-1127-12}{4}$$

Subtract 12 from -1127 to get -1139.

$$-278-\left(-\frac{1139}{4}\right)$$

The opposite of -\frac{1139}{4} is \frac{1139}{4}.

$$-278+\frac{1139}{4}$$

Convert -278 to fraction -\frac{1112}{4}.

$$-\frac{1112}{4}+\frac{1139}{4}$$

Since -\frac{1112}{4} and \frac{1139}{4} have the same denominator, add them by adding their numerators.

$$\frac{-1112+1139}{4}$$

Add -1112 and 1139 to get 27.

$$\frac{27}{4}$$

Factor

$$\frac{3 ^ {3}}{2 ^ {2}} = 6\frac{3}{4} = 6.75$$