Lutasin ang 1.38*10^-23*27.15/sqrt{2*pi*(3.5*10^-10)^2*101*10^5}=

$$\frac { 1.38 \times 10 ^ { - 23 } \times 27.15 } { \sqrt { 2 } \times \pi \times ( 3.5 \times 10 ^ { - 10 } ) ^ { 2 } \times 101 \times 10 ^ { 5 } } =$$

I-evaluate

$$\frac{37467\sqrt{2}}{247450000000000\pi }\approx 6.815953004 \cdot 10^{-11}$$

Mga Hakbang ng Solution

Para magi-divide ng mga power na may parehong base, i-subtract ang exponent ng denominator mula sa exponent ng numerator.

$$\frac{1.38\times 27.15}{101\pi \sqrt{2}\times 10^{28}\times \left(3.5\times 10^{-10}\right)^{2}}$$

I-multiply ang 1.38 at 27.15 para makuha ang 37.467.

$$\frac{37.467}{101\pi \sqrt{2}\times 10^{28}\times \left(3.5\times 10^{-10}\right)^{2}}$$

Kalkulahin ang 10 sa power ng 28 at kunin ang 10000000000000000000000000000.

$$\frac{37.467}{101\pi \sqrt{2}\times 10000000000000000000000000000\times \left(3.5\times 10^{-10}\right)^{2}}$$

I-multiply ang 101 at 10000000000000000000000000000 para makuha ang 1010000000000000000000000000000.

$$\frac{37.467}{1010000000000000000000000000000\pi \sqrt{2}\times \left(3.5\times 10^{-10}\right)^{2}}$$

Kalkulahin ang 10 sa power ng -10 at kunin ang \frac{1}{10000000000}.

$$\frac{37.467}{1010000000000000000000000000000\pi \sqrt{2}\times \left(3.5\times \frac{1}{10000000000}\right)^{2}}$$

I-multiply ang 3.5 at \frac{1}{10000000000} para makuha ang \frac{7}{20000000000}.

$$\frac{37.467}{1010000000000000000000000000000\pi \sqrt{2}\times \left(\frac{7}{20000000000}\right)^{2}}$$

Kalkulahin ang \frac{7}{20000000000} sa power ng 2 at kunin ang \frac{49}{400000000000000000000}.

$$\frac{37.467}{1010000000000000000000000000000\pi \sqrt{2}\times \frac{49}{400000000000000000000}}$$

I-multiply ang 1010000000000000000000000000000 at \frac{49}{400000000000000000000} para makuha ang 123725000000.

$$\frac{37.467}{123725000000\pi \sqrt{2}}$$

I-rationalize ang denominator ng \frac{37.467}{123725000000\pi \sqrt{2}} sa pamamagitan ng pag-multiply ng numerator at denominator sa \sqrt{2}.

$$\frac{37.467\sqrt{2}}{123725000000\pi \left(\sqrt{2}\right)^{2}}$$

Ang square ng \sqrt{2} ay 2.

$$\frac{37.467\sqrt{2}}{123725000000\pi \times 2}$$

I-multiply ang 123725000000 at 2 para makuha ang 247450000000.

$$\frac{37.467\sqrt{2}}{247450000000\pi }$$