Lutasin ang 138*10^-23*2715/sqrt{2*pi*(35*10^-10)^2*101*10^5}=

$$\frac { 138 \times 10 ^ { - 23 } \times 2715 } { \sqrt { 2 } \times \pi \times ( 35 \times 10 ^ { - 10 } ) ^ { 2 } \times 101 \times 10 ^ { 5 } } =$$

I-evaluate

$$\frac{37467\sqrt{2}}{2474500000000\pi }\approx 6.815953004 \cdot 10^{-9}$$

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.

$$\frac{138\times 2715}{101\pi \sqrt{2}\times 10^{28}\times \left(35\times 10^{-10}\right)^{2}}$$

I-multiply ang 138 at 2715 para makuha ang 374670.

$$\frac{374670}{101\pi \sqrt{2}\times 10^{28}\times \left(35\times 10^{-10}\right)^{2}}$$

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

$$\frac{374670}{101\pi \sqrt{2}\times 10000000000000000000000000000\times \left(35\times 10^{-10}\right)^{2}}$$

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

$$\frac{374670}{1010000000000000000000000000000\pi \sqrt{2}\times \left(35\times 10^{-10}\right)^{2}}$$

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

$$\frac{374670}{1010000000000000000000000000000\pi \sqrt{2}\times \left(35\times \frac{1}{10000000000}\right)^{2}}$$

I-multiply ang 35 at \frac{1}{10000000000} para makuha ang \frac{7}{2000000000}.

$$\frac{374670}{1010000000000000000000000000000\pi \sqrt{2}\times \left(\frac{7}{2000000000}\right)^{2}}$$

Kalkulahin ang \frac{7}{2000000000} sa power ng 2 at kunin ang \frac{49}{4000000000000000000}.

$$\frac{374670}{1010000000000000000000000000000\pi \sqrt{2}\times \frac{49}{4000000000000000000}}$$

I-multiply ang 1010000000000000000000000000000 at \frac{49}{4000000000000000000} para makuha ang 12372500000000.

$$\frac{374670}{12372500000000\pi \sqrt{2}}$$

I-rationalize ang denominator ng \frac{374670}{12372500000000\pi \sqrt{2}} sa pamamagitan ng pag-multiply ng numerator at denominator sa \sqrt{2}.

$$\frac{374670\sqrt{2}}{12372500000000\pi \left(\sqrt{2}\right)^{2}}$$

Ang square ng \sqrt{2} ay 2.

$$\frac{374670\sqrt{2}}{12372500000000\pi \times 2}$$

I-cancel out ang 10 sa parehong numerator at denominator.

$$\frac{37467\sqrt{2}}{2\times 1237250000000\pi }$$

I-multiply ang 2 at 1237250000000 para makuha ang 2474500000000.

$$\frac{37467\sqrt{2}}{2474500000000\pi }$$