Solve 6*62*6*10^-24/sqrt{2*1.67*10^-27*81*9*10^-16}

$$\frac { 6 \cdot 62 \cdot 6 \times 10 ^ { - 24 } } { \sqrt { 2 \times 1.67 \times 10 ^ { - 27 } \times 81 \cdot 9 \times 10 ^ { - 16 } } }$$

Evaluate

$$\frac{62\sqrt{835}}{12525}\approx 0.143039898$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -27 and -16 to get -43.

$$\frac{6\times 62\times 6\times 10^{-24}}{\sqrt{2\times 1.67\times 10^{-43}\times 81\times 9}}$$

Multiply 6 and 62 to get 372.

$$\frac{372\times 6\times 10^{-24}}{\sqrt{2\times 1.67\times 10^{-43}\times 81\times 9}}$$

Multiply 372 and 6 to get 2232.

$$\frac{2232\times 10^{-24}}{\sqrt{2\times 1.67\times 10^{-43}\times 81\times 9}}$$

Calculate 10 to the power of -24 and get \frac{1}{1000000000000000000000000}.

$$\frac{2232\times \frac{1}{1000000000000000000000000}}{\sqrt{2\times 1.67\times 10^{-43}\times 81\times 9}}$$

Multiply 2232 and \frac{1}{1000000000000000000000000} to get \frac{279}{125000000000000000000000}.

$$\frac{\frac{279}{125000000000000000000000}}{\sqrt{2\times 1.67\times 10^{-43}\times 81\times 9}}$$

Multiply 2 and 1.67 to get 3.34.

$$\frac{\frac{279}{125000000000000000000000}}{\sqrt{3.34\times 10^{-43}\times 81\times 9}}$$

Calculate 10 to the power of -43 and get \frac{1}{10000000000000000000000000000000000000000000}.

$$\frac{\frac{279}{125000000000000000000000}}{\sqrt{3.34\times \frac{1}{10000000000000000000000000000000000000000000}\times 81\times 9}}$$

Multiply 3.34 and \frac{1}{10000000000000000000000000000000000000000000} to get \frac{167}{500000000000000000000000000000000000000000000}.

$$\frac{\frac{279}{125000000000000000000000}}{\sqrt{\frac{167}{500000000000000000000000000000000000000000000}\times 81\times 9}}$$

Multiply \frac{167}{500000000000000000000000000000000000000000000} and 81 to get \frac{13527}{500000000000000000000000000000000000000000000}.

$$\frac{\frac{279}{125000000000000000000000}}{\sqrt{\frac{13527}{500000000000000000000000000000000000000000000}\times 9}}$$

Multiply \frac{13527}{500000000000000000000000000000000000000000000} and 9 to get \frac{121743}{500000000000000000000000000000000000000000000}.

$$\frac{\frac{279}{125000000000000000000000}}{\sqrt{\frac{121743}{500000000000000000000000000000000000000000000}}}$$

Rewrite the square root of the division \sqrt{\frac{121743}{500000000000000000000000000000000000000000000}} as the division of square roots \frac{\sqrt{121743}}{\sqrt{500000000000000000000000000000000000000000000}}.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{\sqrt{121743}}{\sqrt{500000000000000000000000000000000000000000000}}}$$

Factor 121743=27^{2}\times 167. Rewrite the square root of the product \sqrt{27^{2}\times 167} as the product of square roots \sqrt{27^{2}}\sqrt{167}. Take the square root of 27^{2}.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{27\sqrt{167}}{\sqrt{500000000000000000000000000000000000000000000}}}$$

Factor 500000000000000000000000000000000000000000000=10000000000000000000000^{2}\times 5. Rewrite the square root of the product \sqrt{10000000000000000000000^{2}\times 5} as the product of square roots \sqrt{10000000000000000000000^{2}}\sqrt{5}. Take the square root of 10000000000000000000000^{2}.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{27\sqrt{167}}{10000000000000000000000\sqrt{5}}}$$

Rationalize the denominator of \frac{27\sqrt{167}}{10000000000000000000000\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{27\sqrt{167}\sqrt{5}}{10000000000000000000000\left(\sqrt{5}\right)^{2}}}$$

The square of \sqrt{5} is 5.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{27\sqrt{167}\sqrt{5}}{10000000000000000000000\times 5}}$$

To multiply \sqrt{167} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{27\sqrt{835}}{10000000000000000000000\times 5}}$$

Multiply 10000000000000000000000 and 5 to get 50000000000000000000000.

$$\frac{\frac{279}{125000000000000000000000}}{\frac{27\sqrt{835}}{50000000000000000000000}}$$

Divide \frac{279}{125000000000000000000000} by \frac{27\sqrt{835}}{50000000000000000000000} by multiplying \frac{279}{125000000000000000000000} by the reciprocal of \frac{27\sqrt{835}}{50000000000000000000000}.

$$\frac{279\times 50000000000000000000000}{125000000000000000000000\times 27\sqrt{835}}$$

Cancel out 9\times 25000000000000000000000 in both numerator and denominator.

$$\frac{2\times 31}{3\times 5\sqrt{835}}$$

Rationalize the denominator of \frac{2\times 31}{3\times 5\sqrt{835}} by multiplying numerator and denominator by \sqrt{835}.

$$\frac{2\times 31\sqrt{835}}{3\times 5\left(\sqrt{835}\right)^{2}}$$

The square of \sqrt{835} is 835.

$$\frac{2\times 31\sqrt{835}}{3\times 5\times 835}$$

Multiply 2 and 31 to get 62.

$$\frac{62\sqrt{835}}{3\times 5\times 835}$$

Multiply 3 and 5 to get 15.

$$\frac{62\sqrt{835}}{15\times 835}$$

Multiply 15 and 835 to get 12525.

$$\frac{62\sqrt{835}}{12525}$$