Issolvi frac{12^{4}*12^{7}+frac{36^{11}}{3^{11}}}{12^15/12^11+2^11*6^11}

$$\frac { 12 ^ { 4 } \cdot 12 ^ { 7 } + \frac { 36 ^ { 11 } } { 3 ^ { 11 } } } { \frac { 12 ^ { 15 } } { 12 ^ { 11 } } + 2 ^ { 11 } \cdot 6 ^ { 11 } }$$

Evalwa

$$\frac{71663616}{35831809}\approx 1.999999944$$

Passi tas-Soluzzjonijiet

Biex timmultiplika l-qawwa tal-istess bażi, żid l-esponenti tagħhom. Żid 4 u 7 biex tikseb 11.

$$\frac{12^{11}+\frac{36^{11}}{3^{11}}}{\frac{12^{15}}{12^{11}}+2^{11}\times 6^{11}}$$

Biex tiddividi l-qawwa tal-istess bażi, naqqas l-esponent tad-denominatur mill-esponent tan-numeratur. Naqas 11 minn 15 biex tikseb 4.

$$\frac{12^{11}+\frac{36^{11}}{3^{11}}}{12^{4}+2^{11}\times 6^{11}}$$

Ikkalkula 12 bil-power ta' 11 u tikseb 743008370688.

$$\frac{743008370688+\frac{36^{11}}{3^{11}}}{12^{4}+2^{11}\times 6^{11}}$$

Ikkalkula 36 bil-power ta' 11 u tikseb 131621703842267136.

$$\frac{743008370688+\frac{131621703842267136}{3^{11}}}{12^{4}+2^{11}\times 6^{11}}$$

Ikkalkula 3 bil-power ta' 11 u tikseb 177147.

$$\frac{743008370688+\frac{131621703842267136}{177147}}{12^{4}+2^{11}\times 6^{11}}$$

Iddividi 131621703842267136 b'177147 biex tikseb743008370688.

$$\frac{743008370688+743008370688}{12^{4}+2^{11}\times 6^{11}}$$

Żid 743008370688 u 743008370688 biex tikseb 1486016741376.

$$\frac{1486016741376}{12^{4}+2^{11}\times 6^{11}}$$

Ikkalkula 12 bil-power ta' 4 u tikseb 20736.

$$\frac{1486016741376}{20736+2^{11}\times 6^{11}}$$

Ikkalkula 2 bil-power ta' 11 u tikseb 2048.

$$\frac{1486016741376}{20736+2048\times 6^{11}}$$

Ikkalkula 6 bil-power ta' 11 u tikseb 362797056.

$$\frac{1486016741376}{20736+2048\times 362797056}$$

Immultiplika 2048 u 362797056 biex tikseb 743008370688.

$$\frac{1486016741376}{20736+743008370688}$$

Żid 20736 u 743008370688 biex tikseb 743008391424.

$$\frac{1486016741376}{743008391424}$$

Naqqas il-frazzjoni \frac{1486016741376}{743008391424} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 20736.

$$\frac{71663616}{35831809}$$

Fattur

$$\frac{2 ^ {15} \cdot 3 ^ {7}}{13 \cdot 211 \cdot 13063} = 1\frac{35831807}{35831809} = 1.9999999441836722$$