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

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

Arvuta

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

Lahenduse etapid

Jagage \frac{\left(3a^{5}\right)^{2}}{\left(2b^{4}\right)^{3}} väärtusega \frac{\left(9a^{3}\right)^{2}}{\left(8b^{5}\right)^{3}}, korrutades \frac{\left(3a^{5}\right)^{2}}{\left(2b^{4}\right)^{3}} väärtuse \frac{\left(9a^{3}\right)^{2}}{\left(8b^{5}\right)^{3}} pöördväärtusega.

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

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

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

Astme tõstmiseks mõnda teise astmesse korrutage astendajad. Korrutage 5 ja 2, et saada 10.

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

Arvutage 2 aste 3 ja leidke 9.

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

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

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

Astme tõstmiseks mõnda teise astmesse korrutage astendajad. Korrutage 5 ja 3, et saada 15.

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

Arvutage 3 aste 8 ja leidke 512.

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

Korrutage 9 ja 512, et leida 4608.

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

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

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

Astme tõstmiseks mõnda teise astmesse korrutage astendajad. Korrutage 4 ja 3, et saada 12.

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

Arvutage 3 aste 2 ja leidke 8.

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

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

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

Astme tõstmiseks mõnda teise astmesse korrutage astendajad. Korrutage 3 ja 2, et saada 6.

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

Arvutage 2 aste 9 ja leidke 81.

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

Korrutage 8 ja 81, et leida 648.

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

Taandage 72a^{6}b^{12} nii lugejas kui ka nimetajas.

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

Laienda

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

Lahenduse etapid

Jagage \frac{\left(3a^{5}\right)^{2}}{\left(2b^{4}\right)^{3}} väärtusega \frac{\left(9a^{3}\right)^{2}}{\left(8b^{5}\right)^{3}}, korrutades \frac{\left(3a^{5}\right)^{2}}{\left(2b^{4}\right)^{3}} väärtuse \frac{\left(9a^{3}\right)^{2}}{\left(8b^{5}\right)^{3}} pöördväärtusega.

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

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

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

Astme tõstmiseks mõnda teise astmesse korrutage astendajad. Korrutage 5 ja 2, et saada 10.

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

Arvutage 2 aste 3 ja leidke 9.

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

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

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

Astme tõstmiseks mõnda teise astmesse korrutage astendajad. Korrutage 5 ja 3, et saada 15.

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

Arvutage 3 aste 8 ja leidke 512.

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

Korrutage 9 ja 512, et leida 4608.

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

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

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

Astme tõstmiseks mõnda teise astmesse korrutage astendajad. Korrutage 4 ja 3, et saada 12.

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

Arvutage 3 aste 2 ja leidke 8.

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

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

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

Astme tõstmiseks mõnda teise astmesse korrutage astendajad. Korrutage 3 ja 2, et saada 6.

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

Arvutage 2 aste 9 ja leidke 81.

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

Korrutage 8 ja 81, et leida 648.

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

Taandage 72a^{6}b^{12} nii lugejas kui ka nimetajas.

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