Solve (77.08*7.05+10^-3)-1/1.824+77.08^3/0.128*-10^7

$$\frac { ( 77.08 \times 7.05 + 10 ^ { - 3 } ) - 1 } { 1.824 } + \frac { 77.08 ^ { 3 } } { 0.128 * - 10 ^ { 7 } }$$

Evaluate

$$\frac{112867168885323}{380000000000}\approx 297.018865488$$

Solution Steps

Multiply 77.08 and 7.05 to get 543.414.

$$\frac{543.414+10^{-3}-1}{1.824}+\frac{77.08^{3}}{0.128\left(-10^{7}\right)}$$

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

$$\frac{543.414+\frac{1}{1000}-1}{1.824}+\frac{77.08^{3}}{0.128\left(-10^{7}\right)}$$

Add 543.414 and \frac{1}{1000} to get \frac{108683}{200}.

$$\frac{\frac{108683}{200}-1}{1.824}+\frac{77.08^{3}}{0.128\left(-10^{7}\right)}$$

Subtract 1 from \frac{108683}{200} to get \frac{108483}{200}.

$$\frac{\frac{108483}{200}}{1.824}+\frac{77.08^{3}}{0.128\left(-10^{7}\right)}$$

Express \frac{\frac{108483}{200}}{1.824} as a single fraction.

$$\frac{108483}{200\times 1.824}+\frac{77.08^{3}}{0.128\left(-10^{7}\right)}$$

Multiply 200 and 1.824 to get 364.8.

$$\frac{108483}{364.8}+\frac{77.08^{3}}{0.128\left(-10^{7}\right)}$$

Expand \frac{108483}{364.8} by multiplying both numerator and the denominator by 10.

$$\frac{1084830}{3648}+\frac{77.08^{3}}{0.128\left(-10^{7}\right)}$$

Reduce the fraction \frac{1084830}{3648} to lowest terms by extracting and canceling out 6.

$$\frac{180805}{608}+\frac{77.08^{3}}{0.128\left(-10^{7}\right)}$$

Calculate 77.08 to the power of 3 and get 457957.438912.

$$\frac{180805}{608}+\frac{457957.438912}{0.128\left(-10^{7}\right)}$$

Calculate 10 to the power of 7 and get 10000000.

$$\frac{180805}{608}+\frac{457957.438912}{0.128\left(-10000000\right)}$$

Multiply 0.128 and -10000000 to get -1280000.

$$\frac{180805}{608}+\frac{457957.438912}{-1280000}$$

Expand \frac{457957.438912}{-1280000} by multiplying both numerator and the denominator by 1000000.

$$\frac{180805}{608}+\frac{457957438912}{-1280000000000}$$

Reduce the fraction \frac{457957438912}{-1280000000000} to lowest terms by extracting and canceling out 64.

$$\frac{180805}{608}-\frac{7155584983}{20000000000}$$

Subtract \frac{7155584983}{20000000000} from \frac{180805}{608} to get \frac{112867168885323}{380000000000}.

$$\frac{112867168885323}{380000000000}$$

Factor

$$\frac{3 \cdot 17123 \cdot 2197184467}{19 \cdot 2 ^ {11} \cdot 5 ^ {10}} = 297\frac{7168885323}{380000000000} = 297.0188654876921$$