Solve left(100*10right)^-3sqrt{{left(2*2*10^340/3.6/1.5right)}^2+left(2*200*10^3right)^2}

$${ \left(100 \times 10 \right) }^{ -3 } \sqrt{ { \left( \frac{ 2 \cdot 2 \times 1 { 0 }^{ 3 } \frac{ 40 }{ 3.6 } }{ 1.5 } \right) }^{ 2 } + { \left(2 \cdot 200 \times { 10 }^{ 3 } \right) }^{ 2 } }$$

Evaluate

$$0.0004$$

Solution Steps

Multiply 100 and 10 to get 1000.

$$1000^{-3}\sqrt{\left(\frac{2\times 2\times 1\times 0^{3}\times \frac{40}{3.6}}{1.5}\right)^{2}+\left(2\times 200\times 10^{3}\right)^{2}}$$

Calculate 1000 to the power of -3 and get \frac{1}{1000000000}.

$$\frac{1}{1000000000}\sqrt{\left(\frac{2\times 2\times 1\times 0^{3}\times \frac{40}{3.6}}{1.5}\right)^{2}+\left(2\times 200\times 10^{3}\right)^{2}}$$

Multiply 2 and 2 to get 4.

$$\frac{1}{1000000000}\sqrt{\left(\frac{4\times 1\times 0^{3}\times \frac{40}{3.6}}{1.5}\right)^{2}+\left(2\times 200\times 10^{3}\right)^{2}}$$

Multiply 4 and 1 to get 4.

$$\frac{1}{1000000000}\sqrt{\left(\frac{4\times 0^{3}\times \frac{40}{3.6}}{1.5}\right)^{2}+\left(2\times 200\times 10^{3}\right)^{2}}$$

Calculate 0 to the power of 3 and get 0.

$$\frac{1}{1000000000}\sqrt{\left(\frac{4\times 0\times \frac{40}{3.6}}{1.5}\right)^{2}+\left(2\times 200\times 10^{3}\right)^{2}}$$

Multiply 4 and 0 to get 0.

$$\frac{1}{1000000000}\sqrt{\left(\frac{0\times \frac{40}{3.6}}{1.5}\right)^{2}+\left(2\times 200\times 10^{3}\right)^{2}}$$

Expand \frac{40}{3.6} by multiplying both numerator and the denominator by 10.

$$\frac{1}{1000000000}\sqrt{\left(\frac{0\times \frac{400}{36}}{1.5}\right)^{2}+\left(2\times 200\times 10^{3}\right)^{2}}$$

Reduce the fraction \frac{400}{36} to lowest terms by extracting and canceling out 4.

$$\frac{1}{1000000000}\sqrt{\left(\frac{0\times \frac{100}{9}}{1.5}\right)^{2}+\left(2\times 200\times 10^{3}\right)^{2}}$$

Multiply 0 and \frac{100}{9} to get 0.

$$\frac{1}{1000000000}\sqrt{\left(\frac{0}{1.5}\right)^{2}+\left(2\times 200\times 10^{3}\right)^{2}}$$

Zero divided by any non-zero number gives zero.

$$\frac{1}{1000000000}\sqrt{0^{2}+\left(2\times 200\times 10^{3}\right)^{2}}$$

Calculate 0 to the power of 2 and get 0.

$$\frac{1}{1000000000}\sqrt{0+\left(2\times 200\times 10^{3}\right)^{2}}$$

Multiply 2 and 200 to get 400.

$$\frac{1}{1000000000}\sqrt{0+\left(400\times 10^{3}\right)^{2}}$$

Calculate 10 to the power of 3 and get 1000.

$$\frac{1}{1000000000}\sqrt{0+\left(400\times 1000\right)^{2}}$$

Multiply 400 and 1000 to get 400000.

$$\frac{1}{1000000000}\sqrt{0+400000^{2}}$$

Calculate 400000 to the power of 2 and get 160000000000.

$$\frac{1}{1000000000}\sqrt{0+160000000000}$$

Add 0 and 160000000000 to get 160000000000.

$$\frac{1}{1000000000}\sqrt{160000000000}$$

Calculate the square root of 160000000000 and get 400000.

$$\frac{1}{1000000000}\times 400000$$

Multiply \frac{1}{1000000000} and 400000 to get \frac{1}{2500}.

$$\frac{1}{2500}$$

Factor

$$\frac{1}{2 ^ {2} \cdot 5 ^ {4}} = 0.0004$$