Solve 6.63*10^-34/sqrt{2*9.1*10^-31*3*1.6*10^-19}

$$\frac { 6.63 \times 10 ^ { - 34 } } { \sqrt { 2 \times 9.1 \times 10 ^ { - 31 } \times 3 \times 1.6 \times 10 ^ { - 19 } } }$$

Evaluate

$$\frac{17\sqrt{546}}{560000000000}\approx 7.093445163 \cdot 10^{-10}$$

Solution Steps

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

$$\frac{6.63\times 10^{-34}}{\sqrt{2\times 9.1\times 10^{-50}\times 3\times 1.6}}$$

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

$$\frac{6.63\times \frac{1}{10000000000000000000000000000000000}}{\sqrt{2\times 9.1\times 10^{-50}\times 3\times 1.6}}$$

Multiply 6.63 and \frac{1}{10000000000000000000000000000000000} to get \frac{663}{1000000000000000000000000000000000000}.

$$\frac{\frac{663}{1000000000000000000000000000000000000}}{\sqrt{2\times 9.1\times 10^{-50}\times 3\times 1.6}}$$

Multiply 2 and 9.1 to get 18.2.

$$\frac{\frac{663}{1000000000000000000000000000000000000}}{\sqrt{18.2\times 10^{-50}\times 3\times 1.6}}$$

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

$$\frac{\frac{663}{1000000000000000000000000000000000000}}{\sqrt{18.2\times \frac{1}{100000000000000000000000000000000000000000000000000}\times 3\times 1.6}}$$

Multiply 18.2 and \frac{1}{100000000000000000000000000000000000000000000000000} to get \frac{91}{500000000000000000000000000000000000000000000000000}.

$$\frac{\frac{663}{1000000000000000000000000000000000000}}{\sqrt{\frac{91}{500000000000000000000000000000000000000000000000000}\times 3\times 1.6}}$$

Multiply \frac{91}{500000000000000000000000000000000000000000000000000} and 3 to get \frac{273}{500000000000000000000000000000000000000000000000000}.

$$\frac{\frac{663}{1000000000000000000000000000000000000}}{\sqrt{\frac{273}{500000000000000000000000000000000000000000000000000}\times 1.6}}$$

Multiply \frac{273}{500000000000000000000000000000000000000000000000000} and 1.6 to get \frac{273}{312500000000000000000000000000000000000000000000000}.

$$\frac{\frac{663}{1000000000000000000000000000000000000}}{\sqrt{\frac{273}{312500000000000000000000000000000000000000000000000}}}$$

Rewrite the square root of the division \sqrt{\frac{273}{312500000000000000000000000000000000000000000000000}} as the division of square roots \frac{\sqrt{273}}{\sqrt{312500000000000000000000000000000000000000000000000}}.

$$\frac{\frac{663}{1000000000000000000000000000000000000}}{\frac{\sqrt{273}}{\sqrt{312500000000000000000000000000000000000000000000000}}}$$

Factor 312500000000000000000000000000000000000000000000000=12500000000000000000000000^{2}\times 2. Rewrite the square root of the product \sqrt{12500000000000000000000000^{2}\times 2} as the product of square roots \sqrt{12500000000000000000000000^{2}}\sqrt{2}. Take the square root of 12500000000000000000000000^{2}.

$$\frac{\frac{663}{1000000000000000000000000000000000000}}{\frac{\sqrt{273}}{12500000000000000000000000\sqrt{2}}}$$

Rationalize the denominator of \frac{\sqrt{273}}{12500000000000000000000000\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\frac{663}{1000000000000000000000000000000000000}}{\frac{\sqrt{273}\sqrt{2}}{12500000000000000000000000\left(\sqrt{2}\right)^{2}}}$$

The square of \sqrt{2} is 2.

$$\frac{\frac{663}{1000000000000000000000000000000000000}}{\frac{\sqrt{273}\sqrt{2}}{12500000000000000000000000\times 2}}$$

To multiply \sqrt{273} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\frac{663}{1000000000000000000000000000000000000}}{\frac{\sqrt{546}}{12500000000000000000000000\times 2}}$$

Multiply 12500000000000000000000000 and 2 to get 25000000000000000000000000.

$$\frac{\frac{663}{1000000000000000000000000000000000000}}{\frac{\sqrt{546}}{25000000000000000000000000}}$$

Divide \frac{663}{1000000000000000000000000000000000000} by \frac{\sqrt{546}}{25000000000000000000000000} by multiplying \frac{663}{1000000000000000000000000000000000000} by the reciprocal of \frac{\sqrt{546}}{25000000000000000000000000}.

$$\frac{663\times 25000000000000000000000000}{1000000000000000000000000000000000000\sqrt{546}}$$

Cancel out 25000000000000000000000000 in both numerator and denominator.

$$\frac{663}{40000000000\sqrt{546}}$$

Rationalize the denominator of \frac{663}{40000000000\sqrt{546}} by multiplying numerator and denominator by \sqrt{546}.

$$\frac{663\sqrt{546}}{40000000000\left(\sqrt{546}\right)^{2}}$$

The square of \sqrt{546} is 546.

$$\frac{663\sqrt{546}}{40000000000\times 546}$$

Cancel out 39 in both numerator and denominator.

$$\frac{17\sqrt{546}}{14\times 40000000000}$$

Multiply 14 and 40000000000 to get 560000000000.

$$\frac{17\sqrt{546}}{560000000000}$$