Solve 110^-3/2010^-2+110^-3/810^-2+frac{1{10}^-3}{4{10}^-2}

$$\frac{ 1 { 10 }^{ -3 } }{ 20 { 10 }^{ -2 } } + \frac{ 1 { 10 }^{ -3 } }{ 8 { 10 }^{ -2 } } + \frac{ 1 { 10 }^{ -3 } }{ 4 { 10 }^{ -2 } }$$

Evaluate

$$\frac{17}{400}=0.0425$$

Solution Steps

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{1}{20\times 10^{1}}+\frac{1\times 10^{-3}}{8\times 10^{-2}}+\frac{1\times 10^{-3}}{4\times 10^{-2}}$$

Calculate 10 to the power of 1 and get 10.

$$\frac{1}{20\times 10}+\frac{1\times 10^{-3}}{8\times 10^{-2}}+\frac{1\times 10^{-3}}{4\times 10^{-2}}$$

Multiply 20 and 10 to get 200.

$$\frac{1}{200}+\frac{1\times 10^{-3}}{8\times 10^{-2}}+\frac{1\times 10^{-3}}{4\times 10^{-2}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{1}{200}+\frac{1}{8\times 10^{1}}+\frac{1\times 10^{-3}}{4\times 10^{-2}}$$

Calculate 10 to the power of 1 and get 10.

$$\frac{1}{200}+\frac{1}{8\times 10}+\frac{1\times 10^{-3}}{4\times 10^{-2}}$$

Multiply 8 and 10 to get 80.

$$\frac{1}{200}+\frac{1}{80}+\frac{1\times 10^{-3}}{4\times 10^{-2}}$$

Add \frac{1}{200} and \frac{1}{80} to get \frac{7}{400}.

$$\frac{7}{400}+\frac{1\times 10^{-3}}{4\times 10^{-2}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{7}{400}+\frac{1}{4\times 10^{1}}$$

Calculate 10 to the power of 1 and get 10.

$$\frac{7}{400}+\frac{1}{4\times 10}$$

Multiply 4 and 10 to get 40.

$$\frac{7}{400}+\frac{1}{40}$$

Add \frac{7}{400} and \frac{1}{40} to get \frac{17}{400}.

$$\frac{17}{400}$$

Factor

$$\frac{17}{2 ^ {4} \cdot 5 ^ {2}} = 0.0425$$