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

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

Calcular

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

Pasos da solución

Divide \frac{\left(3a^{5}\right)^{2}}{\left(2b^{4}\right)^{3}} entre \frac{\left(9a^{3}\right)^{2}}{\left(8b^{5}\right)^{3}} mediante a multiplicación de \frac{\left(3a^{5}\right)^{2}}{\left(2b^{4}\right)^{3}} polo recíproco de \frac{\left(9a^{3}\right)^{2}}{\left(8b^{5}\right)^{3}}.

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

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

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

Para elevar unha potencia a outra potencia, multiplica os expoñentes. Multiplica 5 e 2 para obter 10.

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

Calcula 3 á potencia de 2 e obtén 9.

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

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

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

Para elevar unha potencia a outra potencia, multiplica os expoñentes. Multiplica 5 e 3 para obter 15.

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

Calcula 8 á potencia de 3 e obtén 512.

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

Multiplica 9 e 512 para obter 4608.

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

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

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

Para elevar unha potencia a outra potencia, multiplica os expoñentes. Multiplica 4 e 3 para obter 12.

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

Calcula 2 á potencia de 3 e obtén 8.

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

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

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

Para elevar unha potencia a outra potencia, multiplica os expoñentes. Multiplica 3 e 2 para obter 6.

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

Calcula 9 á potencia de 2 e obtén 81.

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

Multiplica 8 e 81 para obter 648.

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

Anula 72a^{6}b^{12} no numerador e no denominador.

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

Expandir

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

Pasos da solución

Divide \frac{\left(3a^{5}\right)^{2}}{\left(2b^{4}\right)^{3}} entre \frac{\left(9a^{3}\right)^{2}}{\left(8b^{5}\right)^{3}} mediante a multiplicación de \frac{\left(3a^{5}\right)^{2}}{\left(2b^{4}\right)^{3}} polo recíproco de \frac{\left(9a^{3}\right)^{2}}{\left(8b^{5}\right)^{3}}.

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

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

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

Para elevar unha potencia a outra potencia, multiplica os expoñentes. Multiplica 5 e 2 para obter 10.

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

Calcula 3 á potencia de 2 e obtén 9.

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

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

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

Para elevar unha potencia a outra potencia, multiplica os expoñentes. Multiplica 5 e 3 para obter 15.

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

Calcula 8 á potencia de 3 e obtén 512.

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

Multiplica 9 e 512 para obter 4608.

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

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

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

Para elevar unha potencia a outra potencia, multiplica os expoñentes. Multiplica 4 e 3 para obter 12.

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

Calcula 2 á potencia de 3 e obtén 8.

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

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

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

Para elevar unha potencia a outra potencia, multiplica os expoñentes. Multiplica 3 e 2 para obter 6.

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

Calcula 9 á potencia de 2 e obtén 81.

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

Multiplica 8 e 81 para obter 648.

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

Anula 72a^{6}b^{12} no numerador e no denominador.

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