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\left(-\frac{3}{2}\right)^{4}\left(a^{3}\right)^{4}\left(b^{2}\right)^{4}\left(-\frac{2}{3}a^{2}b^{3}\right)^{3}
Expand \left(-\frac{3}{2}a^{3}b^{2}\right)^{4}.
\left(-\frac{3}{2}\right)^{4}a^{12}\left(b^{2}\right)^{4}\left(-\frac{2}{3}a^{2}b^{3}\right)^{3}
To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.
\left(-\frac{3}{2}\right)^{4}a^{12}b^{8}\left(-\frac{2}{3}a^{2}b^{3}\right)^{3}
To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.
\frac{81}{16}a^{12}b^{8}\left(-\frac{2}{3}a^{2}b^{3}\right)^{3}
Calculate -\frac{3}{2} to the power of 4 and get \frac{81}{16}.
\frac{81}{16}a^{12}b^{8}\left(-\frac{2}{3}\right)^{3}\left(a^{2}\right)^{3}\left(b^{3}\right)^{3}
Expand \left(-\frac{2}{3}a^{2}b^{3}\right)^{3}.
\frac{81}{16}a^{12}b^{8}\left(-\frac{2}{3}\right)^{3}a^{6}\left(b^{3}\right)^{3}
To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.
\frac{81}{16}a^{12}b^{8}\left(-\frac{2}{3}\right)^{3}a^{6}b^{9}
To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.
\frac{81}{16}a^{12}b^{8}\left(-\frac{8}{27}\right)a^{6}b^{9}
Calculate -\frac{2}{3} to the power of 3 and get -\frac{8}{27}.
-\frac{3}{2}a^{12}b^{8}a^{6}b^{9}
Multiply \frac{81}{16} and -\frac{8}{27} to get -\frac{3}{2}.
-\frac{3}{2}a^{18}b^{8}b^{9}
To multiply powers of the same base, add their exponents. Add 12 and 6 to get 18.
-\frac{3}{2}a^{18}b^{17}
To multiply powers of the same base, add their exponents. Add 8 and 9 to get 17.
\left(-\frac{3}{2}\right)^{4}\left(a^{3}\right)^{4}\left(b^{2}\right)^{4}\left(-\frac{2}{3}a^{2}b^{3}\right)^{3}
Expand \left(-\frac{3}{2}a^{3}b^{2}\right)^{4}.
\left(-\frac{3}{2}\right)^{4}a^{12}\left(b^{2}\right)^{4}\left(-\frac{2}{3}a^{2}b^{3}\right)^{3}
To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.
\left(-\frac{3}{2}\right)^{4}a^{12}b^{8}\left(-\frac{2}{3}a^{2}b^{3}\right)^{3}
To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.
\frac{81}{16}a^{12}b^{8}\left(-\frac{2}{3}a^{2}b^{3}\right)^{3}
Calculate -\frac{3}{2} to the power of 4 and get \frac{81}{16}.
\frac{81}{16}a^{12}b^{8}\left(-\frac{2}{3}\right)^{3}\left(a^{2}\right)^{3}\left(b^{3}\right)^{3}
Expand \left(-\frac{2}{3}a^{2}b^{3}\right)^{3}.
\frac{81}{16}a^{12}b^{8}\left(-\frac{2}{3}\right)^{3}a^{6}\left(b^{3}\right)^{3}
To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.
\frac{81}{16}a^{12}b^{8}\left(-\frac{2}{3}\right)^{3}a^{6}b^{9}
To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.
\frac{81}{16}a^{12}b^{8}\left(-\frac{8}{27}\right)a^{6}b^{9}
Calculate -\frac{2}{3} to the power of 3 and get -\frac{8}{27}.
-\frac{3}{2}a^{12}b^{8}a^{6}b^{9}
Multiply \frac{81}{16} and -\frac{8}{27} to get -\frac{3}{2}.
-\frac{3}{2}a^{18}b^{8}b^{9}
To multiply powers of the same base, add their exponents. Add 12 and 6 to get 18.
-\frac{3}{2}a^{18}b^{17}
To multiply powers of the same base, add their exponents. Add 8 and 9 to get 17.