Solve 6,63*10^-34*10^20/sqrt{2*9.1*10^-31*1.6*10^-9*200}

$$\frac { 6,63 \times 10 ^ { - 34 } \times 10 ^ { 20 } } { \sqrt { 2 \times 9.1 \times 10 ^ { - 31 } \times 1.6 \times 10 ^ { - 9 } \times 200 } }$$

Evaluate

$$\frac{63750\sqrt{91}}{7}\approx 86876.605843329$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -34 and 20 to get -14.

$$\frac{6.63\times 10^{-14}}{\sqrt{2\times 9.1\times 10^{-31}\times 1.6\times 10^{-9}\times 200}}$$

To multiply powers of the same base, add their exponents. Add -31 and -9 to get -40.

$$\frac{6.63\times 10^{-14}}{\sqrt{2\times 9.1\times 10^{-40}\times 1.6\times 200}}$$

Calculate 10 to the power of -14 and get \frac{1}{100000000000000}.

$$\frac{6.63\times \frac{1}{100000000000000}}{\sqrt{2\times 9.1\times 10^{-40}\times 1.6\times 200}}$$

Multiply 6.63 and \frac{1}{100000000000000} to get \frac{663}{10000000000000000}.

$$\frac{\frac{663}{10000000000000000}}{\sqrt{2\times 9.1\times 10^{-40}\times 1.6\times 200}}$$

Multiply 2 and 9.1 to get 18.2.

$$\frac{\frac{663}{10000000000000000}}{\sqrt{18.2\times 10^{-40}\times 1.6\times 200}}$$

Calculate 10 to the power of -40 and get \frac{1}{10000000000000000000000000000000000000000}.

$$\frac{\frac{663}{10000000000000000}}{\sqrt{18.2\times \frac{1}{10000000000000000000000000000000000000000}\times 1.6\times 200}}$$

Multiply 18.2 and \frac{1}{10000000000000000000000000000000000000000} to get \frac{91}{50000000000000000000000000000000000000000}.

$$\frac{\frac{663}{10000000000000000}}{\sqrt{\frac{91}{50000000000000000000000000000000000000000}\times 1.6\times 200}}$$

Multiply \frac{91}{50000000000000000000000000000000000000000} and 1.6 to get \frac{91}{31250000000000000000000000000000000000000}.

$$\frac{\frac{663}{10000000000000000}}{\sqrt{\frac{91}{31250000000000000000000000000000000000000}\times 200}}$$

Multiply \frac{91}{31250000000000000000000000000000000000000} and 200 to get \frac{91}{156250000000000000000000000000000000000}.

$$\frac{\frac{663}{10000000000000000}}{\sqrt{\frac{91}{156250000000000000000000000000000000000}}}$$

Rewrite the square root of the division \sqrt{\frac{91}{156250000000000000000000000000000000000}} as the division of square roots \frac{\sqrt{91}}{\sqrt{156250000000000000000000000000000000000}}.

$$\frac{\frac{663}{10000000000000000}}{\frac{\sqrt{91}}{\sqrt{156250000000000000000000000000000000000}}}$$

Calculate the square root of 156250000000000000000000000000000000000 and get 12500000000000000000.

$$\frac{\frac{663}{10000000000000000}}{\frac{\sqrt{91}}{12500000000000000000}}$$

Divide \frac{663}{10000000000000000} by \frac{\sqrt{91}}{12500000000000000000} by multiplying \frac{663}{10000000000000000} by the reciprocal of \frac{\sqrt{91}}{12500000000000000000}.

$$\frac{663\times 12500000000000000000}{10000000000000000\sqrt{91}}$$

Cancel out 10000000000000000 in both numerator and denominator.

$$\frac{663\times 1250}{\sqrt{91}}$$

Rationalize the denominator of \frac{663\times 1250}{\sqrt{91}} by multiplying numerator and denominator by \sqrt{91}.

$$\frac{663\times 1250\sqrt{91}}{\left(\sqrt{91}\right)^{2}}$$

The square of \sqrt{91} is 91.

$$\frac{663\times 1250\sqrt{91}}{91}$$

Multiply 663 and 1250 to get 828750.

$$\frac{828750\sqrt{91}}{91}$$

Divide 828750\sqrt{91} by 91 to get \frac{63750}{7}\sqrt{91}.

$$\frac{63750}{7}\sqrt{91}$$