Solve 6.6*10^-34/sqrt{2*9.1*10^-31*13.6*1.6*10^-18}

$$\frac { 6.6 \times 10 ^ { - 34 } } { \sqrt { 2 \times 9.1 \times 10 ^ { - 31 } \times 13.6 \times 1.6 \times 10 ^ { - 18 } } }$$

Evaluate

$$\frac{33\sqrt{1547}}{12376000000000}\approx 1.048766475 \cdot 10^{-10}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -31 and -18 to get -49.

$$\frac{6.6\times 10^{-34}}{\sqrt{2\times 9.1\times 10^{-49}\times 13.6\times 1.6}}$$

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

$$\frac{6.6\times \frac{1}{10000000000000000000000000000000000}}{\sqrt{2\times 9.1\times 10^{-49}\times 13.6\times 1.6}}$$

Multiply 6.6 and \frac{1}{10000000000000000000000000000000000} to get \frac{33}{50000000000000000000000000000000000}.

$$\frac{\frac{33}{50000000000000000000000000000000000}}{\sqrt{2\times 9.1\times 10^{-49}\times 13.6\times 1.6}}$$

Multiply 2 and 9.1 to get 18.2.

$$\frac{\frac{33}{50000000000000000000000000000000000}}{\sqrt{18.2\times 10^{-49}\times 13.6\times 1.6}}$$

Calculate 10 to the power of -49 and get \frac{1}{10000000000000000000000000000000000000000000000000}.

$$\frac{\frac{33}{50000000000000000000000000000000000}}{\sqrt{18.2\times \frac{1}{10000000000000000000000000000000000000000000000000}\times 13.6\times 1.6}}$$

Multiply 18.2 and \frac{1}{10000000000000000000000000000000000000000000000000} to get \frac{91}{50000000000000000000000000000000000000000000000000}.

$$\frac{\frac{33}{50000000000000000000000000000000000}}{\sqrt{\frac{91}{50000000000000000000000000000000000000000000000000}\times 13.6\times 1.6}}$$

Multiply \frac{91}{50000000000000000000000000000000000000000000000000} and 13.6 to get \frac{1547}{62500000000000000000000000000000000000000000000000}.

$$\frac{\frac{33}{50000000000000000000000000000000000}}{\sqrt{\frac{1547}{62500000000000000000000000000000000000000000000000}\times 1.6}}$$

Multiply \frac{1547}{62500000000000000000000000000000000000000000000000} and 1.6 to get \frac{1547}{39062500000000000000000000000000000000000000000000}.

$$\frac{\frac{33}{50000000000000000000000000000000000}}{\sqrt{\frac{1547}{39062500000000000000000000000000000000000000000000}}}$$

Rewrite the square root of the division \sqrt{\frac{1547}{39062500000000000000000000000000000000000000000000}} as the division of square roots \frac{\sqrt{1547}}{\sqrt{39062500000000000000000000000000000000000000000000}}.

$$\frac{\frac{33}{50000000000000000000000000000000000}}{\frac{\sqrt{1547}}{\sqrt{39062500000000000000000000000000000000000000000000}}}$$

Calculate the square root of 39062500000000000000000000000000000000000000000000 and get 6250000000000000000000000.

$$\frac{\frac{33}{50000000000000000000000000000000000}}{\frac{\sqrt{1547}}{6250000000000000000000000}}$$

Divide \frac{33}{50000000000000000000000000000000000} by \frac{\sqrt{1547}}{6250000000000000000000000} by multiplying \frac{33}{50000000000000000000000000000000000} by the reciprocal of \frac{\sqrt{1547}}{6250000000000000000000000}.

$$\frac{33\times 6250000000000000000000000}{50000000000000000000000000000000000\sqrt{1547}}$$

Cancel out 6250000000000000000000000 in both numerator and denominator.

$$\frac{33}{8000000000\sqrt{1547}}$$

Rationalize the denominator of \frac{33}{8000000000\sqrt{1547}} by multiplying numerator and denominator by \sqrt{1547}.

$$\frac{33\sqrt{1547}}{8000000000\left(\sqrt{1547}\right)^{2}}$$

The square of \sqrt{1547} is 1547.

$$\frac{33\sqrt{1547}}{8000000000\times 1547}$$

Multiply 8000000000 and 1547 to get 12376000000000.

$$\frac{33\sqrt{1547}}{12376000000000}$$