Lahenda [{(80001)^2div(1001)^2}*91]div2=?

$$[ \{ ( 80001 ) ^ { 2 } \div ( 1001 ) ^ { 2 } \} \times 91 ] \div 2 = ?$$

Arvuta

$$\frac{6400160001}{22022}\approx 290625,737943874$$

Lahenduse etapid

Arvutage 2 aste 80001 ja leidke 6400160001.

$$\frac{\frac{6400160001}{1001^{2}}\times 91}{2}$$

Arvutage 2 aste 1001 ja leidke 1002001.

$$\frac{\frac{6400160001}{1002001}\times 91}{2}$$

Avaldage \frac{6400160001}{1002001}\times 91 ühe murdarvuna.

$$\frac{\frac{6400160001\times 91}{1002001}}{2}$$

Korrutage 6400160001 ja 91, et leida 582414560091.

$$\frac{\frac{582414560091}{1002001}}{2}$$

Taandage murd \frac{582414560091}{1002001} vähimale ühiskordsele, eraldades ja taandades arvu 91.

$$\frac{\frac{6400160001}{11011}}{2}$$

Avaldage \frac{\frac{6400160001}{11011}}{2} ühe murdarvuna.

$$\frac{6400160001}{11011\times 2}$$

Korrutage 11011 ja 2, et leida 22022.

$$\frac{6400160001}{22022}$$

Lahuta teguriteks

$$\frac{3 ^ {6} \cdot 2963 ^ {2}}{2 \cdot 7 \cdot 11 ^ {2} \cdot 13} = 290625\frac{16251}{22022} = 290625,7379438743$$