Issolvi frac{(3a^{5})^{2}}{(2b^{4})^{3}}:(9a^3)^2/(8b^5)^3

$$\frac { ( 3 a ^ { 5 } ) ^ { 2 } } { ( 2 b ^ { 4 } ) ^ { 3 } } : \frac { ( 9 a ^ { 3 } ) ^ { 2 } } { ( 8 b ^ { 5 } ) ^ { 3 } }$$

Evalwa

$$\frac{64b^{3}a^{4}}{9}$$

Passi tas-Soluzzjonijiet

Iddividi \frac{\left(3a^{5}\right)^{2}}{\left(2b^{4}\right)^{3}} b'\frac{\left(9a^{3}\right)^{2}}{\left(8b^{5}\right)^{3}} billi timmultiplika \frac{\left(3a^{5}\right)^{2}}{\left(2b^{4}\right)^{3}} bir-reċiproku ta' \frac{\left(9a^{3}\right)^{2}}{\left(8b^{5}\right)^{3}}.

$$\frac{\left(3a^{5}\right)^{2}\times \left(8b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Espandi \left(3a^{5}\right)^{2}.

$$\frac{3^{2}\left(a^{5}\right)^{2}\times \left(8b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Biex tgħolli l-qawwa ta' numru għal qawwa oħra, immultiplika l-esponenti. Immultiplika 5 u 2 biex tikseb 10.

$$\frac{3^{2}a^{10}\times \left(8b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Ikkalkula 3 bil-power ta' 2 u tikseb 9.

$$\frac{9a^{10}\times \left(8b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Espandi \left(8b^{5}\right)^{3}.

$$\frac{9a^{10}\times 8^{3}\left(b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Biex tgħolli l-qawwa ta' numru għal qawwa oħra, immultiplika l-esponenti. Immultiplika 5 u 3 biex tikseb 15.

$$\frac{9a^{10}\times 8^{3}b^{15}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Ikkalkula 8 bil-power ta' 3 u tikseb 512.

$$\frac{9a^{10}\times 512b^{15}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Immultiplika 9 u 512 biex tikseb 4608.

$$\frac{4608a^{10}b^{15}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Espandi \left(2b^{4}\right)^{3}.

$$\frac{4608a^{10}b^{15}}{2^{3}\left(b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Biex tgħolli l-qawwa ta' numru għal qawwa oħra, immultiplika l-esponenti. Immultiplika 4 u 3 biex tikseb 12.

$$\frac{4608a^{10}b^{15}}{2^{3}b^{12}\times \left(9a^{3}\right)^{2}}$$

Ikkalkula 2 bil-power ta' 3 u tikseb 8.

$$\frac{4608a^{10}b^{15}}{8b^{12}\times \left(9a^{3}\right)^{2}}$$

Espandi \left(9a^{3}\right)^{2}.

$$\frac{4608a^{10}b^{15}}{8b^{12}\times 9^{2}\left(a^{3}\right)^{2}}$$

Biex tgħolli l-qawwa ta' numru għal qawwa oħra, immultiplika l-esponenti. Immultiplika 3 u 2 biex tikseb 6.

$$\frac{4608a^{10}b^{15}}{8b^{12}\times 9^{2}a^{6}}$$

Ikkalkula 9 bil-power ta' 2 u tikseb 81.

$$\frac{4608a^{10}b^{15}}{8b^{12}\times 81a^{6}}$$

Immultiplika 8 u 81 biex tikseb 648.

$$\frac{4608a^{10}b^{15}}{648b^{12}a^{6}}$$

Annulla 72a^{6}b^{12} fin-numeratur u d-denominatur.

$$\frac{64b^{3}a^{4}}{9}$$

Espandi

$$\frac{64b^{3}a^{4}}{9}$$

Passi tas-Soluzzjonijiet

Iddividi \frac{\left(3a^{5}\right)^{2}}{\left(2b^{4}\right)^{3}} b'\frac{\left(9a^{3}\right)^{2}}{\left(8b^{5}\right)^{3}} billi timmultiplika \frac{\left(3a^{5}\right)^{2}}{\left(2b^{4}\right)^{3}} bir-reċiproku ta' \frac{\left(9a^{3}\right)^{2}}{\left(8b^{5}\right)^{3}}.

$$\frac{\left(3a^{5}\right)^{2}\times \left(8b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Espandi \left(3a^{5}\right)^{2}.

$$\frac{3^{2}\left(a^{5}\right)^{2}\times \left(8b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Biex tgħolli l-qawwa ta' numru għal qawwa oħra, immultiplika l-esponenti. Immultiplika 5 u 2 biex tikseb 10.

$$\frac{3^{2}a^{10}\times \left(8b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Ikkalkula 3 bil-power ta' 2 u tikseb 9.

$$\frac{9a^{10}\times \left(8b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Espandi \left(8b^{5}\right)^{3}.

$$\frac{9a^{10}\times 8^{3}\left(b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Biex tgħolli l-qawwa ta' numru għal qawwa oħra, immultiplika l-esponenti. Immultiplika 5 u 3 biex tikseb 15.

$$\frac{9a^{10}\times 8^{3}b^{15}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Ikkalkula 8 bil-power ta' 3 u tikseb 512.

$$\frac{9a^{10}\times 512b^{15}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Immultiplika 9 u 512 biex tikseb 4608.

$$\frac{4608a^{10}b^{15}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Espandi \left(2b^{4}\right)^{3}.

$$\frac{4608a^{10}b^{15}}{2^{3}\left(b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}$$

Biex tgħolli l-qawwa ta' numru għal qawwa oħra, immultiplika l-esponenti. Immultiplika 4 u 3 biex tikseb 12.

$$\frac{4608a^{10}b^{15}}{2^{3}b^{12}\times \left(9a^{3}\right)^{2}}$$

Ikkalkula 2 bil-power ta' 3 u tikseb 8.

$$\frac{4608a^{10}b^{15}}{8b^{12}\times \left(9a^{3}\right)^{2}}$$

Espandi \left(9a^{3}\right)^{2}.

$$\frac{4608a^{10}b^{15}}{8b^{12}\times 9^{2}\left(a^{3}\right)^{2}}$$

Biex tgħolli l-qawwa ta' numru għal qawwa oħra, immultiplika l-esponenti. Immultiplika 3 u 2 biex tikseb 6.

$$\frac{4608a^{10}b^{15}}{8b^{12}\times 9^{2}a^{6}}$$

Ikkalkula 9 bil-power ta' 2 u tikseb 81.

$$\frac{4608a^{10}b^{15}}{8b^{12}\times 81a^{6}}$$

Immultiplika 8 u 81 biex tikseb 648.

$$\frac{4608a^{10}b^{15}}{648b^{12}a^{6}}$$

Annulla 72a^{6}b^{12} fin-numeratur u d-denominatur.

$$\frac{64b^{3}a^{4}}{9}$$