Løs 316*9*10^9left(16*10^-19right)^2/664*10^-27{left(5*{10^7right)}^-2}

$$\frac{ 316 \cdot 9 \times { 10 }^{ 9 } { \left(16 \times { 10 }^{ -19 } \right) }^{ 2 } }{ 664 \times { 10 }^{ -27 } { \left(5 \times { 10 }^{ 7 } \right) }^{ -2 } }$$

Evaluer

$$\frac{2275200000000000000}{83}\approx 2,741204819 \cdot 10^{16}$$

Løsningsvejledning

Udlign 4 i både tælleren og nævneren.

$$\frac{9\times 79\times 10^{9}\times \left(16\times 10^{-19}\right)^{2}}{166\times 10^{-27}\times \left(5\times 10^{7}\right)^{-2}}$$

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

$$\frac{9\times 79\times 10^{36}\times \left(16\times 10^{-19}\right)^{2}}{166\times \left(5\times 10^{7}\right)^{-2}}$$

Multiplicer 9 og 79 for at få 711.

$$\frac{711\times 10^{36}\times \left(16\times 10^{-19}\right)^{2}}{166\times \left(5\times 10^{7}\right)^{-2}}$$

Beregn 10 til potensen af 36, og få 1000000000000000000000000000000000000.

$$\frac{711\times 1000000000000000000000000000000000000\times \left(16\times 10^{-19}\right)^{2}}{166\times \left(5\times 10^{7}\right)^{-2}}$$

Multiplicer 711 og 1000000000000000000000000000000000000 for at få 711000000000000000000000000000000000000.

$$\frac{711000000000000000000000000000000000000\times \left(16\times 10^{-19}\right)^{2}}{166\times \left(5\times 10^{7}\right)^{-2}}$$

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

$$\frac{711000000000000000000000000000000000000\times \left(16\times \frac{1}{10000000000000000000}\right)^{2}}{166\times \left(5\times 10^{7}\right)^{-2}}$$

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

$$\frac{711000000000000000000000000000000000000\times \left(\frac{1}{625000000000000000}\right)^{2}}{166\times \left(5\times 10^{7}\right)^{-2}}$$

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

$$\frac{711000000000000000000000000000000000000\times \frac{1}{390625000000000000000000000000000000}}{166\times \left(5\times 10^{7}\right)^{-2}}$$

Multiplicer 711000000000000000000000000000000000000 og \frac{1}{390625000000000000000000000000000000} for at få \frac{45504}{25}.

$$\frac{\frac{45504}{25}}{166\times \left(5\times 10^{7}\right)^{-2}}$$

Beregn 10 til potensen af 7, og få 10000000.

$$\frac{\frac{45504}{25}}{166\times \left(5\times 10000000\right)^{-2}}$$

Multiplicer 5 og 10000000 for at få 50000000.

$$\frac{\frac{45504}{25}}{166\times 50000000^{-2}}$$

Beregn 50000000 til potensen af -2, og få \frac{1}{2500000000000000}.

$$\frac{\frac{45504}{25}}{166\times \frac{1}{2500000000000000}}$$

Multiplicer 166 og \frac{1}{2500000000000000} for at få \frac{83}{1250000000000000}.

$$\frac{\frac{45504}{25}}{\frac{83}{1250000000000000}}$$

Divider \frac{45504}{25} med \frac{83}{1250000000000000} ved at multiplicere \frac{45504}{25} med den reciprokke værdi af \frac{83}{1250000000000000}.

$$\frac{45504}{25}\times \frac{1250000000000000}{83}$$

Multiplicer \frac{45504}{25} og \frac{1250000000000000}{83} for at få \frac{2275200000000000000}{83}.

$$\frac{2275200000000000000}{83}$$

Faktoriser

$$\frac{2 ^ {19} \cdot 3 ^ {2} \cdot 5 ^ {14} \cdot 79}{83} = 27412048192771084\frac{28}{83} = 27412048192771084$$