Løs left(3546+10^-5right)^9/left(505*10^2right)^12

$$\frac{ { \left(3546+ { 10 }^{ -5 } \right) }^{ 9 } }{ { \left(505 \times { 10 }^{ 2 } \right) }^{ 12 } }$$

Evaluer

$$\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{275103767122062920083301025390625000000000000000000000000000000000000000000000000000000000000000000000}\approx 3,222196748 \cdot 10^{-25}$$

Løsningsvejledning

Beregn 10 til potensen af -5, og få \frac{1}{100000}.

$$\frac{\left(3546+\frac{1}{100000}\right)^{9}}{\left(505\times 10^{2}\right)^{12}}$$

Tilføj 3546 og \frac{1}{100000} for at få \frac{354600001}{100000}.

$$\frac{\left(\frac{354600001}{100000}\right)^{9}}{\left(505\times 10^{2}\right)^{12}}$$

Beregn \frac{354600001}{100000} til potensen af 9, og få \frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000}.

$$\frac{\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000}}{\left(505\times 10^{2}\right)^{12}}$$

Beregn 10 til potensen af 2, og få 100.

$$\frac{\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000}}{\left(505\times 100\right)^{12}}$$

Multiplicer 505 og 100 for at få 50500.

$$\frac{\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000}}{50500^{12}}$$

Beregn 50500 til potensen af 12, og få 275103767122062920083301025390625000000000000000000000000.

$$\frac{\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000}}{275103767122062920083301025390625000000000000000000000000}$$

Udtryk \frac{\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000}}{275103767122062920083301025390625000000000000000000000000} som en enkelt brøk.

$$\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{1000000000000000000000000000000000000000000000\times 275103767122062920083301025390625000000000000000000000000}$$

Multiplicer 1000000000000000000000000000000000000000000000 og 275103767122062920083301025390625000000000000000000000000 for at få 275103767122062920083301025390625000000000000000000000000000000000000000000000000000000000000000000000.

$$\frac{88643846374063778992669503139207124783046594447907591722092750681763191400001}{275103767122062920083301025390625000000000000000000000000000000000000000000000000000000000000000000000}$$