Solve (frac{6.626*10^{-34}*9*4.6*10^-7}{8*3*10^8*1.77*10^-25})^frac{1{2}}=

$$( \frac { 6.626 \times 10 ^ { - 34 } \times 9 \times 4.6 \times 10 ^ { - 7 } } { 8 \times 3 \times 10 ^ { 8 } \times 1.77 \times 10 ^ { - 25 } } ) ^ { \frac { 1 } { 2 } } =$$

Evaluate

$$\frac{\sqrt{8991482}}{1180000000000000}\approx 2.541169489 \cdot 10^{-12}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -34 and -7 to get -41.

$$\left(\frac{6.626\times 10^{-41}\times 9\times 4.6}{8\times 3\times 10^{8}\times 1.77\times 10^{-25}}\right)^{\frac{1}{2}}$$

To multiply powers of the same base, add their exponents. Add 8 and -25 to get -17.

$$\left(\frac{6.626\times 10^{-41}\times 9\times 4.6}{8\times 3\times 10^{-17}\times 1.77}\right)^{\frac{1}{2}}$$

Cancel out 3 in both numerator and denominator.

$$\left(\frac{3\times 4.6\times 6.626\times 10^{-41}}{1.77\times 8\times 10^{-17}}\right)^{\frac{1}{2}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\left(\frac{3\times 4.6\times 6.626}{1.77\times 8\times 10^{24}}\right)^{\frac{1}{2}}$$

Multiply 3 and 4.6 to get 13.8.

$$\left(\frac{13.8\times 6.626}{1.77\times 8\times 10^{24}}\right)^{\frac{1}{2}}$$

Multiply 13.8 and 6.626 to get 91.4388.

$$\left(\frac{91.4388}{1.77\times 8\times 10^{24}}\right)^{\frac{1}{2}}$$

Multiply 1.77 and 8 to get 14.16.

$$\left(\frac{91.4388}{14.16\times 10^{24}}\right)^{\frac{1}{2}}$$

Calculate 10 to the power of 24 and get 1000000000000000000000000.

$$\left(\frac{91.4388}{14.16\times 1000000000000000000000000}\right)^{\frac{1}{2}}$$

Multiply 14.16 and 1000000000000000000000000 to get 14160000000000000000000000.

$$\left(\frac{91.4388}{14160000000000000000000000}\right)^{\frac{1}{2}}$$

Expand \frac{91.4388}{14160000000000000000000000} by multiplying both numerator and the denominator by 10000.

$$\left(\frac{914388}{141600000000000000000000000000}\right)^{\frac{1}{2}}$$

Reduce the fraction \frac{914388}{141600000000000000000000000000} to lowest terms by extracting and canceling out 12.

$$\left(\frac{76199}{11800000000000000000000000000}\right)^{\frac{1}{2}}$$