Solve (3*10^{-3})^{2}*10*10^{3}+(1*10^-3)^2*20*10^3+32*13*10^-3

$$( 3 \times 10 ^ { - 3 } ) ^ { 2 } \times 10 \times 10 ^ { 3 } + ( 1 \times 10 ^ { - 3 } ) ^ { 2 } \times 20 \times 10 ^ { 3 } + 32 \times 13 \times 10 ^ { - 3 }$$

Evaluate

$$\frac{263}{500}=0.526$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\left(3\times 10^{-3}\right)^{2}\times 10^{4}+\left(1\times 10^{-3}\right)^{2}\times 20\times 10^{3}+32\times 13\times 10^{-3}$$

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

$$\left(3\times \frac{1}{1000}\right)^{2}\times 10^{4}+\left(1\times 10^{-3}\right)^{2}\times 20\times 10^{3}+32\times 13\times 10^{-3}$$

Multiply 3 and \frac{1}{1000} to get \frac{3}{1000}.

$$\left(\frac{3}{1000}\right)^{2}\times 10^{4}+\left(1\times 10^{-3}\right)^{2}\times 20\times 10^{3}+32\times 13\times 10^{-3}$$

Calculate \frac{3}{1000} to the power of 2 and get \frac{9}{1000000}.

$$\frac{9}{1000000}\times 10^{4}+\left(1\times 10^{-3}\right)^{2}\times 20\times 10^{3}+32\times 13\times 10^{-3}$$

Calculate 10 to the power of 4 and get 10000.

$$\frac{9}{1000000}\times 10000+\left(1\times 10^{-3}\right)^{2}\times 20\times 10^{3}+32\times 13\times 10^{-3}$$

Multiply \frac{9}{1000000} and 10000 to get \frac{9}{100}.

$$\frac{9}{100}+\left(1\times 10^{-3}\right)^{2}\times 20\times 10^{3}+32\times 13\times 10^{-3}$$

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

$$\frac{9}{100}+\left(1\times \frac{1}{1000}\right)^{2}\times 20\times 10^{3}+32\times 13\times 10^{-3}$$

Multiply 1 and \frac{1}{1000} to get \frac{1}{1000}.

$$\frac{9}{100}+\left(\frac{1}{1000}\right)^{2}\times 20\times 10^{3}+32\times 13\times 10^{-3}$$

Calculate \frac{1}{1000} to the power of 2 and get \frac{1}{1000000}.

$$\frac{9}{100}+\frac{1}{1000000}\times 20\times 10^{3}+32\times 13\times 10^{-3}$$

Multiply \frac{1}{1000000} and 20 to get \frac{1}{50000}.

$$\frac{9}{100}+\frac{1}{50000}\times 10^{3}+32\times 13\times 10^{-3}$$

Calculate 10 to the power of 3 and get 1000.

$$\frac{9}{100}+\frac{1}{50000}\times 1000+32\times 13\times 10^{-3}$$

Multiply \frac{1}{50000} and 1000 to get \frac{1}{50}.

$$\frac{9}{100}+\frac{1}{50}+32\times 13\times 10^{-3}$$

Add \frac{9}{100} and \frac{1}{50} to get \frac{11}{100}.

$$\frac{11}{100}+32\times 13\times 10^{-3}$$

Multiply 32 and 13 to get 416.

$$\frac{11}{100}+416\times 10^{-3}$$

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

$$\frac{11}{100}+416\times \frac{1}{1000}$$

Multiply 416 and \frac{1}{1000} to get \frac{52}{125}.

$$\frac{11}{100}+\frac{52}{125}$$

Add \frac{11}{100} and \frac{52}{125} to get \frac{263}{500}.

$$\frac{263}{500}$$

Factor

$$\frac{263}{2 ^ {2} \cdot 5 ^ {3}} = 0.526$$