Løs 4*pi^2*left(228*10^8right)^3divleft(687*24*60*60right)^2/372*{6794^2div4}

$$\frac{ 4 \times { \pi }^{ 2 } \times { \left(228 \times { 10 }^{ 8 } \right) }^{ 3 } \div { \left(687 \times 24 \times 60 \times 60 \right) }^{ 2 } }{ 372 \times { 6794 }^{ 2 } \div 4 }$$

Evaluer

$$\frac{42868750000000000000000\pi ^{2}}{13675754015223831}\approx 30937789,843119998$$

Løsningsvejledning

Divider \frac{4\pi ^{2}\times \left(228\times 10^{8}\right)^{3}}{\left(687\times 24\times 60\times 60\right)^{2}} med \frac{372\times 6794^{2}}{4} ved at multiplicere \frac{4\pi ^{2}\times \left(228\times 10^{8}\right)^{3}}{\left(687\times 24\times 60\times 60\right)^{2}} med den reciprokke værdi af \frac{372\times 6794^{2}}{4}.

$$\frac{4\pi ^{2}\times \left(228\times 10^{8}\right)^{3}\times 4}{\left(687\times 24\times 60\times 60\right)^{2}\times 372\times 6794^{2}}$$

Udlign 4 i både tælleren og nævneren.

$$\frac{4\pi ^{2}\times \left(228\times 10^{8}\right)^{3}}{93\times 6794^{2}\times \left(24\times 60\times 60\times 687\right)^{2}}$$

Beregn 10 til potensen af 8, og få 100000000.

$$\frac{4\pi ^{2}\times \left(228\times 100000000\right)^{3}}{93\times 6794^{2}\times \left(24\times 60\times 60\times 687\right)^{2}}$$

Multiplicer 228 og 100000000 for at få 22800000000.

$$\frac{4\pi ^{2}\times 22800000000^{3}}{93\times 6794^{2}\times \left(24\times 60\times 60\times 687\right)^{2}}$$

Beregn 22800000000 til potensen af 3, og få 11852352000000000000000000000000.

$$\frac{4\pi ^{2}\times 11852352000000000000000000000000}{93\times 6794^{2}\times \left(24\times 60\times 60\times 687\right)^{2}}$$

Multiplicer 4 og 11852352000000000000000000000000 for at få 47409408000000000000000000000000.

$$\frac{47409408000000000000000000000000\pi ^{2}}{93\times 6794^{2}\times \left(24\times 60\times 60\times 687\right)^{2}}$$

Beregn 6794 til potensen af 2, og få 46158436.

$$\frac{47409408000000000000000000000000\pi ^{2}}{93\times 46158436\times \left(24\times 60\times 60\times 687\right)^{2}}$$

Multiplicer 93 og 46158436 for at få 4292734548.

$$\frac{47409408000000000000000000000000\pi ^{2}}{4292734548\times \left(24\times 60\times 60\times 687\right)^{2}}$$

Multiplicer 24 og 60 for at få 1440.

$$\frac{47409408000000000000000000000000\pi ^{2}}{4292734548\times \left(1440\times 60\times 687\right)^{2}}$$

Multiplicer 1440 og 60 for at få 86400.

$$\frac{47409408000000000000000000000000\pi ^{2}}{4292734548\times \left(86400\times 687\right)^{2}}$$

Multiplicer 86400 og 687 for at få 59356800.

$$\frac{47409408000000000000000000000000\pi ^{2}}{4292734548\times 59356800^{2}}$$

Beregn 59356800 til potensen af 2, og få 3523229706240000.

$$\frac{47409408000000000000000000000000\pi ^{2}}{4292734548\times 3523229706240000}$$

Multiplicer 4292734548 og 3523229706240000 for at få 15124289880516339179520000.

$$\frac{47409408000000000000000000000000\pi ^{2}}{15124289880516339179520000}$$

Divider 47409408000000000000000000000000\pi ^{2} med 15124289880516339179520000 for at få \frac{42868750000000000000000}{13675754015223831}\pi ^{2}.

$$\frac{42868750000000000000000}{13675754015223831}\pi ^{2}$$

Udvid

$$\frac{42868750000000000000000 \pi ^ {2}}{13675754015223831} = 30937789\frac{11530301708766792}{13675754015223832} = 30937789,843119998$$

Løsningsvejledning

Divider \frac{4\pi ^{2}\times \left(228\times 10^{8}\right)^{3}}{\left(687\times 24\times 60\times 60\right)^{2}} med \frac{372\times 6794^{2}}{4} ved at multiplicere \frac{4\pi ^{2}\times \left(228\times 10^{8}\right)^{3}}{\left(687\times 24\times 60\times 60\right)^{2}} med den reciprokke værdi af \frac{372\times 6794^{2}}{4}.

$$\frac{4\pi ^{2}\times \left(228\times 10^{8}\right)^{3}\times 4}{\left(687\times 24\times 60\times 60\right)^{2}\times 372\times 6794^{2}}$$

Udlign 4 i både tælleren og nævneren.

$$\frac{4\pi ^{2}\times \left(228\times 10^{8}\right)^{3}}{93\times 6794^{2}\times \left(24\times 60\times 60\times 687\right)^{2}}$$

Beregn 10 til potensen af 8, og få 100000000.

$$\frac{4\pi ^{2}\times \left(228\times 100000000\right)^{3}}{93\times 6794^{2}\times \left(24\times 60\times 60\times 687\right)^{2}}$$

Multiplicer 228 og 100000000 for at få 22800000000.

$$\frac{4\pi ^{2}\times 22800000000^{3}}{93\times 6794^{2}\times \left(24\times 60\times 60\times 687\right)^{2}}$$

Beregn 22800000000 til potensen af 3, og få 11852352000000000000000000000000.

$$\frac{4\pi ^{2}\times 11852352000000000000000000000000}{93\times 6794^{2}\times \left(24\times 60\times 60\times 687\right)^{2}}$$

Multiplicer 4 og 11852352000000000000000000000000 for at få 47409408000000000000000000000000.

$$\frac{47409408000000000000000000000000\pi ^{2}}{93\times 6794^{2}\times \left(24\times 60\times 60\times 687\right)^{2}}$$

Beregn 6794 til potensen af 2, og få 46158436.

$$\frac{47409408000000000000000000000000\pi ^{2}}{93\times 46158436\times \left(24\times 60\times 60\times 687\right)^{2}}$$

Multiplicer 93 og 46158436 for at få 4292734548.

$$\frac{47409408000000000000000000000000\pi ^{2}}{4292734548\times \left(24\times 60\times 60\times 687\right)^{2}}$$

Multiplicer 24 og 60 for at få 1440.

$$\frac{47409408000000000000000000000000\pi ^{2}}{4292734548\times \left(1440\times 60\times 687\right)^{2}}$$

Multiplicer 1440 og 60 for at få 86400.

$$\frac{47409408000000000000000000000000\pi ^{2}}{4292734548\times \left(86400\times 687\right)^{2}}$$

Multiplicer 86400 og 687 for at få 59356800.

$$\frac{47409408000000000000000000000000\pi ^{2}}{4292734548\times 59356800^{2}}$$

Beregn 59356800 til potensen af 2, og få 3523229706240000.

$$\frac{47409408000000000000000000000000\pi ^{2}}{4292734548\times 3523229706240000}$$

Multiplicer 4292734548 og 3523229706240000 for at få 15124289880516339179520000.

$$\frac{47409408000000000000000000000000\pi ^{2}}{15124289880516339179520000}$$

Divider 47409408000000000000000000000000\pi ^{2} med 15124289880516339179520000 for at få \frac{42868750000000000000000}{13675754015223831}\pi ^{2}.

$$\frac{42868750000000000000000}{13675754015223831}\pi ^{2}$$