Solve 6.625*10^-34/sqrt{2*9.109*10^-31*1.602*10^19}*1/sqrt{150}

$$\frac { 6.625 \times 10 ^ { - 34 } } { \sqrt { 2 \times 9.109 \times 10 ^ { - 31 } \times 1.602 \times 10 ^ { 19 } } } \times \frac { 1 } { \sqrt { 150 } }$$

Evaluate

$$\frac{53\sqrt{4864206}}{11674094400000000000000000000000000}\approx 1.001287163 \cdot 10^{-29}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -31 and 19 to get -12.

$$\frac{6.625\times 10^{-34}}{\sqrt{2\times 9.109\times 10^{-12}\times 1.602}}\times \frac{1}{\sqrt{150}}$$

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

$$\frac{6.625\times \frac{1}{10000000000000000000000000000000000}}{\sqrt{2\times 9.109\times 10^{-12}\times 1.602}}\times \frac{1}{\sqrt{150}}$$

Multiply 6.625 and \frac{1}{10000000000000000000000000000000000} to get \frac{53}{80000000000000000000000000000000000}.

$$\frac{\frac{53}{80000000000000000000000000000000000}}{\sqrt{2\times 9.109\times 10^{-12}\times 1.602}}\times \frac{1}{\sqrt{150}}$$

Multiply 2 and 9.109 to get 18.218.

$$\frac{\frac{53}{80000000000000000000000000000000000}}{\sqrt{18.218\times 10^{-12}\times 1.602}}\times \frac{1}{\sqrt{150}}$$

Calculate 10 to the power of -12 and get \frac{1}{1000000000000}.

$$\frac{\frac{53}{80000000000000000000000000000000000}}{\sqrt{18.218\times \frac{1}{1000000000000}\times 1.602}}\times \frac{1}{\sqrt{150}}$$

Multiply 18.218 and \frac{1}{1000000000000} to get \frac{9109}{500000000000000}.

$$\frac{\frac{53}{80000000000000000000000000000000000}}{\sqrt{\frac{9109}{500000000000000}\times 1.602}}\times \frac{1}{\sqrt{150}}$$

Multiply \frac{9109}{500000000000000} and 1.602 to get \frac{7296309}{250000000000000000}.

$$\frac{\frac{53}{80000000000000000000000000000000000}}{\sqrt{\frac{7296309}{250000000000000000}}}\times \frac{1}{\sqrt{150}}$$

Rewrite the square root of the division \sqrt{\frac{7296309}{250000000000000000}} as the division of square roots \frac{\sqrt{7296309}}{\sqrt{250000000000000000}}.

$$\frac{\frac{53}{80000000000000000000000000000000000}}{\frac{\sqrt{7296309}}{\sqrt{250000000000000000}}}\times \frac{1}{\sqrt{150}}$$

Factor 7296309=3^{2}\times 810701. Rewrite the square root of the product \sqrt{3^{2}\times 810701} as the product of square roots \sqrt{3^{2}}\sqrt{810701}. Take the square root of 3^{2}.

$$\frac{\frac{53}{80000000000000000000000000000000000}}{\frac{3\sqrt{810701}}{\sqrt{250000000000000000}}}\times \frac{1}{\sqrt{150}}$$

Calculate the square root of 250000000000000000 and get 500000000.

$$\frac{\frac{53}{80000000000000000000000000000000000}}{\frac{3\sqrt{810701}}{500000000}}\times \frac{1}{\sqrt{150}}$$

Divide \frac{53}{80000000000000000000000000000000000} by \frac{3\sqrt{810701}}{500000000} by multiplying \frac{53}{80000000000000000000000000000000000} by the reciprocal of \frac{3\sqrt{810701}}{500000000}.

$$\frac{53\times 500000000}{80000000000000000000000000000000000\times 3\sqrt{810701}}\times \frac{1}{\sqrt{150}}$$

Cancel out 500000000 in both numerator and denominator.

$$\frac{53}{3\times 160000000000000000000000000\sqrt{810701}}\times \frac{1}{\sqrt{150}}$$

Rationalize the denominator of \frac{53}{3\times 160000000000000000000000000\sqrt{810701}} by multiplying numerator and denominator by \sqrt{810701}.

$$\frac{53\sqrt{810701}}{3\times 160000000000000000000000000\left(\sqrt{810701}\right)^{2}}\times \frac{1}{\sqrt{150}}$$

The square of \sqrt{810701} is 810701.

$$\frac{53\sqrt{810701}}{3\times 160000000000000000000000000\times 810701}\times \frac{1}{\sqrt{150}}$$

Multiply 3 and 160000000000000000000000000 to get 480000000000000000000000000.

$$\frac{53\sqrt{810701}}{480000000000000000000000000\times 810701}\times \frac{1}{\sqrt{150}}$$

Multiply 480000000000000000000000000 and 810701 to get 389136480000000000000000000000000.

$$\frac{53\sqrt{810701}}{389136480000000000000000000000000}\times \frac{1}{\sqrt{150}}$$

Factor 150=5^{2}\times 6. Rewrite the square root of the product \sqrt{5^{2}\times 6} as the product of square roots \sqrt{5^{2}}\sqrt{6}. Take the square root of 5^{2}.

$$\frac{53\sqrt{810701}}{389136480000000000000000000000000}\times \frac{1}{5\sqrt{6}}$$

Rationalize the denominator of \frac{1}{5\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{53\sqrt{810701}}{389136480000000000000000000000000}\times \frac{\sqrt{6}}{5\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{53\sqrt{810701}}{389136480000000000000000000000000}\times \frac{\sqrt{6}}{5\times 6}$$

Multiply 5 and 6 to get 30.

$$\frac{53\sqrt{810701}}{389136480000000000000000000000000}\times \frac{\sqrt{6}}{30}$$

Multiply \frac{53\sqrt{810701}}{389136480000000000000000000000000} times \frac{\sqrt{6}}{30} by multiplying numerator times numerator and denominator times denominator.

$$\frac{53\sqrt{810701}\sqrt{6}}{389136480000000000000000000000000\times 30}$$

To multiply \sqrt{810701} and \sqrt{6}, multiply the numbers under the square root.

$$\frac{53\sqrt{4864206}}{389136480000000000000000000000000\times 30}$$

Multiply 389136480000000000000000000000000 and 30 to get 11674094400000000000000000000000000.

$$\frac{53\sqrt{4864206}}{11674094400000000000000000000000000}$$