Solve (26+500*5.46*10^-3-28.6*10^4*500^-2)-(26+300*5.46*10^-3-28.6*{10}^4*{300}^-2)

$$(26+500 \times 5.46 \times { 10 }^{ -3 } -28.6 \times { 10 }^{ 4 } \times { 500 }^{ -2 } )-(26+300 \times 5.46 \times { 10 }^{ -3 } -28.6 \times { 10 }^{ 4 } \times { 300 }^{ -2 } )$$

Evaluate

$$\frac{7033}{2250}\approx 3.125777778$$

Solution Steps

Multiply 500 and 5.46 to get 2730.

$$26+2730\times 10^{-3}-28.6\times 10^{4}\times 500^{-2}-\left(26+300\times 5.46\times 10^{-3}-28.6\times 10^{4}\times 300^{-2}\right)$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$26+2730\times \frac{1}{1000}-28.6\times 10^{4}\times 500^{-2}-\left(26+300\times 5.46\times 10^{-3}-28.6\times 10^{4}\times 300^{-2}\right)$$

Multiply 2730 and \frac{1}{1000} to get \frac{273}{100}.

$$26+\frac{273}{100}-28.6\times 10^{4}\times 500^{-2}-\left(26+300\times 5.46\times 10^{-3}-28.6\times 10^{4}\times 300^{-2}\right)$$

Add 26 and \frac{273}{100} to get \frac{2873}{100}.

$$\frac{2873}{100}-28.6\times 10^{4}\times 500^{-2}-\left(26+300\times 5.46\times 10^{-3}-28.6\times 10^{4}\times 300^{-2}\right)$$

Calculate 10 to the power of 4 and get 10000.

$$\frac{2873}{100}-28.6\times 10000\times 500^{-2}-\left(26+300\times 5.46\times 10^{-3}-28.6\times 10^{4}\times 300^{-2}\right)$$

Multiply 28.6 and 10000 to get 286000.

$$\frac{2873}{100}-286000\times 500^{-2}-\left(26+300\times 5.46\times 10^{-3}-28.6\times 10^{4}\times 300^{-2}\right)$$

Calculate 500 to the power of -2 and get \frac{1}{250000}.

$$\frac{2873}{100}-286000\times \frac{1}{250000}-\left(26+300\times 5.46\times 10^{-3}-28.6\times 10^{4}\times 300^{-2}\right)$$

Multiply 286000 and \frac{1}{250000} to get \frac{143}{125}.

$$\frac{2873}{100}-\frac{143}{125}-\left(26+300\times 5.46\times 10^{-3}-28.6\times 10^{4}\times 300^{-2}\right)$$

Subtract \frac{143}{125} from \frac{2873}{100} to get \frac{13793}{500}.

$$\frac{13793}{500}-\left(26+300\times 5.46\times 10^{-3}-28.6\times 10^{4}\times 300^{-2}\right)$$

Multiply 300 and 5.46 to get 1638.

$$\frac{13793}{500}-\left(26+1638\times 10^{-3}-28.6\times 10^{4}\times 300^{-2}\right)$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{13793}{500}-\left(26+1638\times \frac{1}{1000}-28.6\times 10^{4}\times 300^{-2}\right)$$

Multiply 1638 and \frac{1}{1000} to get \frac{819}{500}.

$$\frac{13793}{500}-\left(26+\frac{819}{500}-28.6\times 10^{4}\times 300^{-2}\right)$$

Add 26 and \frac{819}{500} to get \frac{13819}{500}.

$$\frac{13793}{500}-\left(\frac{13819}{500}-28.6\times 10^{4}\times 300^{-2}\right)$$

Calculate 10 to the power of 4 and get 10000.

$$\frac{13793}{500}-\left(\frac{13819}{500}-28.6\times 10000\times 300^{-2}\right)$$

Multiply 28.6 and 10000 to get 286000.

$$\frac{13793}{500}-\left(\frac{13819}{500}-286000\times 300^{-2}\right)$$

Calculate 300 to the power of -2 and get \frac{1}{90000}.

$$\frac{13793}{500}-\left(\frac{13819}{500}-286000\times \frac{1}{90000}\right)$$

Multiply 286000 and \frac{1}{90000} to get \frac{143}{45}.

$$\frac{13793}{500}-\left(\frac{13819}{500}-\frac{143}{45}\right)$$

Subtract \frac{143}{45} from \frac{13819}{500} to get \frac{110071}{4500}.

$$\frac{13793}{500}-\frac{110071}{4500}$$

Subtract \frac{110071}{4500} from \frac{13793}{500} to get \frac{7033}{2250}.

$$\frac{7033}{2250}$$

Factor

$$\frac{13 \cdot 541}{2 \cdot 3 ^ {2} \cdot 5 ^ {3}} = 3\frac{283}{2250} = 3.125777777777778$$