Solve sqrt{2*885*10^-1407*119/1610^-19}sqrt{1/10^17}

$$\sqrt{ \frac{ 2 \cdot 885 \times { 10 }^{ -14 } 07 \cdot 119 }{ 16 { 10 }^{ -19 } } } \sqrt{ \frac{ 1 }{ { 10 }^{ 17 } } }$$

Evaluate

$$0$$

Solution Steps

Cancel out 2\times 8 in both numerator and denominator.

$$\sqrt{\frac{0}{10^{-19}}}\sqrt{\frac{1}{10^{17}}}$$

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

$$\sqrt{0}\sqrt{\frac{1}{10^{17}}}$$

Calculate the square root of 0 and get 0.

$$0\sqrt{\frac{1}{10^{17}}}$$

Calculate 10 to the power of 17 and get 100000000000000000.

$$0\sqrt{\frac{1}{100000000000000000}}$$

Rewrite the square root of the division \sqrt{\frac{1}{100000000000000000}} as the division of square roots \frac{\sqrt{1}}{\sqrt{100000000000000000}}.

$$0\times \frac{\sqrt{1}}{\sqrt{100000000000000000}}$$

Calculate the square root of 1 and get 1.

$$0\times \frac{1}{\sqrt{100000000000000000}}$$

Factor 100000000000000000=100000000^{2}\times 10. Rewrite the square root of the product \sqrt{100000000^{2}\times 10} as the product of square roots \sqrt{100000000^{2}}\sqrt{10}. Take the square root of 100000000^{2}.

$$0\times \frac{1}{100000000\sqrt{10}}$$

Rationalize the denominator of \frac{1}{100000000\sqrt{10}} by multiplying numerator and denominator by \sqrt{10}.

$$0\times \frac{\sqrt{10}}{100000000\left(\sqrt{10}\right)^{2}}$$

The square of \sqrt{10} is 10.

$$0\times \frac{\sqrt{10}}{100000000\times 10}$$

Multiply 100000000 and 10 to get 1000000000.

$$0\times \frac{\sqrt{10}}{1000000000}$$

Anything times zero gives zero.

$$0$$

Factor

$$0$$