Solve 6*6*10^-34/sqrt{2*9*1*10^-31*1.6*10^-19}

$$\frac { 6 \cdot 6 \times 10 ^ { - 34 } } { \sqrt { 2 \times 9 \cdot 1 \times 10 ^ { - 31 } \times 1.6 \times 10 ^ { - 19 } } }$$

Evaluate

$$\frac{3\sqrt{5}}{1000000000}\approx 6.708203932 \cdot 10^{-9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -31 and -19 to get -50.

$$\frac{6\times 6\times 10^{-34}}{\sqrt{2\times 9\times 1\times 10^{-50}\times 1.6}}$$

Multiply 6 and 6 to get 36.

$$\frac{36\times 10^{-34}}{\sqrt{2\times 9\times 1\times 10^{-50}\times 1.6}}$$

Calculate 10 to the power of -34 and get \frac{1}{10000000000000000000000000000000000}.

$$\frac{36\times \frac{1}{10000000000000000000000000000000000}}{\sqrt{2\times 9\times 1\times 10^{-50}\times 1.6}}$$

Multiply 36 and \frac{1}{10000000000000000000000000000000000} to get \frac{9}{2500000000000000000000000000000000}.

$$\frac{\frac{9}{2500000000000000000000000000000000}}{\sqrt{2\times 9\times 1\times 10^{-50}\times 1.6}}$$

Multiply 2 and 9 to get 18.

$$\frac{\frac{9}{2500000000000000000000000000000000}}{\sqrt{18\times 1\times 10^{-50}\times 1.6}}$$

Multiply 18 and 1 to get 18.

$$\frac{\frac{9}{2500000000000000000000000000000000}}{\sqrt{18\times 10^{-50}\times 1.6}}$$

Calculate 10 to the power of -50 and get \frac{1}{100000000000000000000000000000000000000000000000000}.

$$\frac{\frac{9}{2500000000000000000000000000000000}}{\sqrt{18\times \frac{1}{100000000000000000000000000000000000000000000000000}\times 1.6}}$$

Multiply 18 and \frac{1}{100000000000000000000000000000000000000000000000000} to get \frac{9}{50000000000000000000000000000000000000000000000000}.

$$\frac{\frac{9}{2500000000000000000000000000000000}}{\sqrt{\frac{9}{50000000000000000000000000000000000000000000000000}\times 1.6}}$$

Multiply \frac{9}{50000000000000000000000000000000000000000000000000} and 1.6 to get \frac{9}{31250000000000000000000000000000000000000000000000}.

$$\frac{\frac{9}{2500000000000000000000000000000000}}{\sqrt{\frac{9}{31250000000000000000000000000000000000000000000000}}}$$

Rewrite the square root of the division \sqrt{\frac{9}{31250000000000000000000000000000000000000000000000}} as the division of square roots \frac{\sqrt{9}}{\sqrt{31250000000000000000000000000000000000000000000000}}.

$$\frac{\frac{9}{2500000000000000000000000000000000}}{\frac{\sqrt{9}}{\sqrt{31250000000000000000000000000000000000000000000000}}}$$

Calculate the square root of 9 and get 3.

$$\frac{\frac{9}{2500000000000000000000000000000000}}{\frac{3}{\sqrt{31250000000000000000000000000000000000000000000000}}}$$

Factor 31250000000000000000000000000000000000000000000000=2500000000000000000000000^{2}\times 5. Rewrite the square root of the product \sqrt{2500000000000000000000000^{2}\times 5} as the product of square roots \sqrt{2500000000000000000000000^{2}}\sqrt{5}. Take the square root of 2500000000000000000000000^{2}.

$$\frac{\frac{9}{2500000000000000000000000000000000}}{\frac{3}{2500000000000000000000000\sqrt{5}}}$$

Rationalize the denominator of \frac{3}{2500000000000000000000000\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\frac{9}{2500000000000000000000000000000000}}{\frac{3\sqrt{5}}{2500000000000000000000000\left(\sqrt{5}\right)^{2}}}$$

The square of \sqrt{5} is 5.

$$\frac{\frac{9}{2500000000000000000000000000000000}}{\frac{3\sqrt{5}}{2500000000000000000000000\times 5}}$$

Multiply 2500000000000000000000000 and 5 to get 12500000000000000000000000.

$$\frac{\frac{9}{2500000000000000000000000000000000}}{\frac{3\sqrt{5}}{12500000000000000000000000}}$$

Divide \frac{9}{2500000000000000000000000000000000} by \frac{3\sqrt{5}}{12500000000000000000000000} by multiplying \frac{9}{2500000000000000000000000000000000} by the reciprocal of \frac{3\sqrt{5}}{12500000000000000000000000}.

$$\frac{9\times 12500000000000000000000000}{2500000000000000000000000000000000\times 3\sqrt{5}}$$

Cancel out 3\times 12500000000000000000000000 in both numerator and denominator.

$$\frac{3}{200000000\sqrt{5}}$$

Rationalize the denominator of \frac{3}{200000000\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{3\sqrt{5}}{200000000\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{3\sqrt{5}}{200000000\times 5}$$

Multiply 200000000 and 5 to get 1000000000.

$$\frac{3\sqrt{5}}{1000000000}$$