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\frac{\left(3a^{5}\right)^{2}\times \left(8b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}
Divide \frac{\left(3a^{5}\right)^{2}}{\left(2b^{4}\right)^{3}} by \frac{\left(9a^{3}\right)^{2}}{\left(8b^{5}\right)^{3}} by multiplying \frac{\left(3a^{5}\right)^{2}}{\left(2b^{4}\right)^{3}} by the reciprocal of \frac{\left(9a^{3}\right)^{2}}{\left(8b^{5}\right)^{3}}.
\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}}
Expand \left(3a^{5}\right)^{2}.
\frac{3^{2}a^{10}\times \left(8b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}
To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.
\frac{9a^{10}\times \left(8b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}
Calculate 3 to the power of 2 and get 9.
\frac{9a^{10}\times 8^{3}\left(b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}
Expand \left(8b^{5}\right)^{3}.
\frac{9a^{10}\times 8^{3}b^{15}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}
To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.
\frac{9a^{10}\times 512b^{15}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}
Calculate 8 to the power of 3 and get 512.
\frac{4608a^{10}b^{15}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}
Multiply 9 and 512 to get 4608.
\frac{4608a^{10}b^{15}}{2^{3}\left(b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}
Expand \left(2b^{4}\right)^{3}.
\frac{4608a^{10}b^{15}}{2^{3}b^{12}\times \left(9a^{3}\right)^{2}}
To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.
\frac{4608a^{10}b^{15}}{8b^{12}\times \left(9a^{3}\right)^{2}}
Calculate 2 to the power of 3 and get 8.
\frac{4608a^{10}b^{15}}{8b^{12}\times 9^{2}\left(a^{3}\right)^{2}}
Expand \left(9a^{3}\right)^{2}.
\frac{4608a^{10}b^{15}}{8b^{12}\times 9^{2}a^{6}}
To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.
\frac{4608a^{10}b^{15}}{8b^{12}\times 81a^{6}}
Calculate 9 to the power of 2 and get 81.
\frac{4608a^{10}b^{15}}{648b^{12}a^{6}}
Multiply 8 and 81 to get 648.
\frac{64b^{3}a^{4}}{9}
Cancel out 72a^{6}b^{12} in both numerator and denominator.
\frac{\left(3a^{5}\right)^{2}\times \left(8b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}
Divide \frac{\left(3a^{5}\right)^{2}}{\left(2b^{4}\right)^{3}} by \frac{\left(9a^{3}\right)^{2}}{\left(8b^{5}\right)^{3}} by multiplying \frac{\left(3a^{5}\right)^{2}}{\left(2b^{4}\right)^{3}} by the reciprocal of \frac{\left(9a^{3}\right)^{2}}{\left(8b^{5}\right)^{3}}.
\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}}
Expand \left(3a^{5}\right)^{2}.
\frac{3^{2}a^{10}\times \left(8b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}
To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.
\frac{9a^{10}\times \left(8b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}
Calculate 3 to the power of 2 and get 9.
\frac{9a^{10}\times 8^{3}\left(b^{5}\right)^{3}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}
Expand \left(8b^{5}\right)^{3}.
\frac{9a^{10}\times 8^{3}b^{15}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}
To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.
\frac{9a^{10}\times 512b^{15}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}
Calculate 8 to the power of 3 and get 512.
\frac{4608a^{10}b^{15}}{\left(2b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}
Multiply 9 and 512 to get 4608.
\frac{4608a^{10}b^{15}}{2^{3}\left(b^{4}\right)^{3}\times \left(9a^{3}\right)^{2}}
Expand \left(2b^{4}\right)^{3}.
\frac{4608a^{10}b^{15}}{2^{3}b^{12}\times \left(9a^{3}\right)^{2}}
To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.
\frac{4608a^{10}b^{15}}{8b^{12}\times \left(9a^{3}\right)^{2}}
Calculate 2 to the power of 3 and get 8.
\frac{4608a^{10}b^{15}}{8b^{12}\times 9^{2}\left(a^{3}\right)^{2}}
Expand \left(9a^{3}\right)^{2}.
\frac{4608a^{10}b^{15}}{8b^{12}\times 9^{2}a^{6}}
To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.
\frac{4608a^{10}b^{15}}{8b^{12}\times 81a^{6}}
Calculate 9 to the power of 2 and get 81.
\frac{4608a^{10}b^{15}}{648b^{12}a^{6}}
Multiply 8 and 81 to get 648.
\frac{64b^{3}a^{4}}{9}
Cancel out 72a^{6}b^{12} in both numerator and denominator.