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\frac{\left(3a^{2}\right)^{5}\times \left(9a^{4}\right)^{2}b^{15}}{\left(27a^{2}\right)^{3}\left(b^{5}\right)^{3}}
To raise a power to another power, multiply the exponents. Multiply 3 and 5 to get 15.
\frac{\left(3a^{2}\right)^{5}\times \left(9a^{4}\right)^{2}b^{15}}{\left(27a^{2}\right)^{3}b^{15}}
To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.
\frac{\left(9a^{4}\right)^{2}\times \left(3a^{2}\right)^{5}}{\left(27a^{2}\right)^{3}}
Cancel out b^{15} in both numerator and denominator.
\frac{9^{2}\left(a^{4}\right)^{2}\times \left(3a^{2}\right)^{5}}{\left(27a^{2}\right)^{3}}
Expand \left(9a^{4}\right)^{2}.
\frac{9^{2}a^{8}\times \left(3a^{2}\right)^{5}}{\left(27a^{2}\right)^{3}}
To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.
\frac{81a^{8}\times \left(3a^{2}\right)^{5}}{\left(27a^{2}\right)^{3}}
Calculate 9 to the power of 2 and get 81.
\frac{81a^{8}\times 3^{5}\left(a^{2}\right)^{5}}{\left(27a^{2}\right)^{3}}
Expand \left(3a^{2}\right)^{5}.
\frac{81a^{8}\times 3^{5}a^{10}}{\left(27a^{2}\right)^{3}}
To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.
\frac{81a^{8}\times 243a^{10}}{\left(27a^{2}\right)^{3}}
Calculate 3 to the power of 5 and get 243.
\frac{19683a^{8}a^{10}}{\left(27a^{2}\right)^{3}}
Multiply 81 and 243 to get 19683.
\frac{19683a^{18}}{\left(27a^{2}\right)^{3}}
To multiply powers of the same base, add their exponents. Add 8 and 10 to get 18.
\frac{19683a^{18}}{27^{3}\left(a^{2}\right)^{3}}
Expand \left(27a^{2}\right)^{3}.
\frac{19683a^{18}}{27^{3}a^{6}}
To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.
\frac{19683a^{18}}{19683a^{6}}
Calculate 27 to the power of 3 and get 19683.
a^{12}
Cancel out 19683a^{6} in both numerator and denominator.
\frac{\left(3a^{2}\right)^{5}\times \left(9a^{4}\right)^{2}b^{15}}{\left(27a^{2}\right)^{3}\left(b^{5}\right)^{3}}
To raise a power to another power, multiply the exponents. Multiply 3 and 5 to get 15.
\frac{\left(3a^{2}\right)^{5}\times \left(9a^{4}\right)^{2}b^{15}}{\left(27a^{2}\right)^{3}b^{15}}
To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.
\frac{\left(9a^{4}\right)^{2}\times \left(3a^{2}\right)^{5}}{\left(27a^{2}\right)^{3}}
Cancel out b^{15} in both numerator and denominator.
\frac{9^{2}\left(a^{4}\right)^{2}\times \left(3a^{2}\right)^{5}}{\left(27a^{2}\right)^{3}}
Expand \left(9a^{4}\right)^{2}.
\frac{9^{2}a^{8}\times \left(3a^{2}\right)^{5}}{\left(27a^{2}\right)^{3}}
To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.
\frac{81a^{8}\times \left(3a^{2}\right)^{5}}{\left(27a^{2}\right)^{3}}
Calculate 9 to the power of 2 and get 81.
\frac{81a^{8}\times 3^{5}\left(a^{2}\right)^{5}}{\left(27a^{2}\right)^{3}}
Expand \left(3a^{2}\right)^{5}.
\frac{81a^{8}\times 3^{5}a^{10}}{\left(27a^{2}\right)^{3}}
To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.
\frac{81a^{8}\times 243a^{10}}{\left(27a^{2}\right)^{3}}
Calculate 3 to the power of 5 and get 243.
\frac{19683a^{8}a^{10}}{\left(27a^{2}\right)^{3}}
Multiply 81 and 243 to get 19683.
\frac{19683a^{18}}{\left(27a^{2}\right)^{3}}
To multiply powers of the same base, add their exponents. Add 8 and 10 to get 18.
\frac{19683a^{18}}{27^{3}\left(a^{2}\right)^{3}}
Expand \left(27a^{2}\right)^{3}.
\frac{19683a^{18}}{27^{3}a^{6}}
To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.
\frac{19683a^{18}}{19683a^{6}}
Calculate 27 to the power of 3 and get 19683.
a^{12}
Cancel out 19683a^{6} in both numerator and denominator.