Løs frac{9*10^{9}*(16*10^{-19})^2}{667*10^11*91*10^-31*166*10^-27}

$$\frac { 9 \times 10 ^ { 9 } \times ( 16 \times 10 ^ { - 19 } ) ^ { 2 } } { 667 \times 10 ^ { 11 } \times 91 \times 10 ^ { - 31 } \times 166 \times 10 ^ { - 27 } }$$

Evaluer

$$\frac{1152000000000000000000}{5037851}\approx 2,286689305 \cdot 10^{14}$$

Løsningsvejledning

Hvis du vil gange potenser for den samme base, skal du tilføje deres eksponenter. Tilføj 11 og -31 for at få -20.

$$\frac{9\times 10^{9}\times \left(16\times 10^{-19}\right)^{2}}{667\times 10^{-20}\times 91\times 166\times 10^{-27}}$$

Hvis du vil gange potenser for den samme base, skal du tilføje deres eksponenter. Tilføj -20 og -27 for at få -47.

$$\frac{9\times 10^{9}\times \left(16\times 10^{-19}\right)^{2}}{667\times 10^{-47}\times 91\times 166}$$

Hvis du vil dividere potenserne for samme base, skal du subtrahere nævnerens eksponent fra tællerens eksponent.

$$\frac{9\times 10^{56}\times \left(16\times 10^{-19}\right)^{2}}{91\times 166\times 667}$$

Beregn 10 til potensen af 56, og få 100000000000000000000000000000000000000000000000000000000.

$$\frac{9\times 100000000000000000000000000000000000000000000000000000000\times \left(16\times 10^{-19}\right)^{2}}{91\times 166\times 667}$$

Multiplicer 9 og 100000000000000000000000000000000000000000000000000000000 for at få 900000000000000000000000000000000000000000000000000000000.

$$\frac{900000000000000000000000000000000000000000000000000000000\times \left(16\times 10^{-19}\right)^{2}}{91\times 166\times 667}$$

Beregn 10 til potensen af -19, og få \frac{1}{10000000000000000000}.

$$\frac{900000000000000000000000000000000000000000000000000000000\times \left(16\times \frac{1}{10000000000000000000}\right)^{2}}{91\times 166\times 667}$$

Multiplicer 16 og \frac{1}{10000000000000000000} for at få \frac{1}{625000000000000000}.

$$\frac{900000000000000000000000000000000000000000000000000000000\times \left(\frac{1}{625000000000000000}\right)^{2}}{91\times 166\times 667}$$

Beregn \frac{1}{625000000000000000} til potensen af 2, og få \frac{1}{390625000000000000000000000000000000}.

$$\frac{900000000000000000000000000000000000000000000000000000000\times \frac{1}{390625000000000000000000000000000000}}{91\times 166\times 667}$$

Multiplicer 900000000000000000000000000000000000000000000000000000000 og \frac{1}{390625000000000000000000000000000000} for at få 2304000000000000000000.

$$\frac{2304000000000000000000}{91\times 166\times 667}$$

Multiplicer 91 og 166 for at få 15106.

$$\frac{2304000000000000000000}{15106\times 667}$$

Multiplicer 15106 og 667 for at få 10075702.

$$\frac{2304000000000000000000}{10075702}$$

Reducer fraktionen \frac{2304000000000000000000}{10075702} til de laveste led ved at udtrække og annullere 2.

$$\frac{1152000000000000000000}{5037851}$$

Faktoriser

$$\frac{2 ^ {25} \cdot 3 ^ {2} \cdot 5 ^ {18}}{7 \cdot 13 \cdot 23 \cdot 29 \cdot 83} = 228668930462611\frac{4711039}{5037851} = 228668930462611,94$$