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\left(6ab^{2}\right)^{2}c\times \left(2bc^{3}\right)^{3}
Multiply 2 and 3 to get 6.
6^{2}a^{2}\left(b^{2}\right)^{2}c\times \left(2bc^{3}\right)^{3}
Expand \left(6ab^{2}\right)^{2}.
6^{2}a^{2}b^{4}c\times \left(2bc^{3}\right)^{3}
To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.
36a^{2}b^{4}c\times \left(2bc^{3}\right)^{3}
Calculate 6 to the power of 2 and get 36.
36a^{2}b^{4}c\times 2^{3}b^{3}\left(c^{3}\right)^{3}
Expand \left(2bc^{3}\right)^{3}.
36a^{2}b^{4}c\times 2^{3}b^{3}c^{9}
To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.
36a^{2}b^{4}c\times 8b^{3}c^{9}
Calculate 2 to the power of 3 and get 8.
288a^{2}b^{4}cb^{3}c^{9}
Multiply 36 and 8 to get 288.
288a^{2}b^{7}cc^{9}
To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.
288a^{2}b^{7}c^{10}
To multiply powers of the same base, add their exponents. Add 1 and 9 to get 10.
\left(6ab^{2}\right)^{2}c\times \left(2bc^{3}\right)^{3}
Multiply 2 and 3 to get 6.
6^{2}a^{2}\left(b^{2}\right)^{2}c\times \left(2bc^{3}\right)^{3}
Expand \left(6ab^{2}\right)^{2}.
6^{2}a^{2}b^{4}c\times \left(2bc^{3}\right)^{3}
To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.
36a^{2}b^{4}c\times \left(2bc^{3}\right)^{3}
Calculate 6 to the power of 2 and get 36.
36a^{2}b^{4}c\times 2^{3}b^{3}\left(c^{3}\right)^{3}
Expand \left(2bc^{3}\right)^{3}.
36a^{2}b^{4}c\times 2^{3}b^{3}c^{9}
To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.
36a^{2}b^{4}c\times 8b^{3}c^{9}
Calculate 2 to the power of 3 and get 8.
288a^{2}b^{4}cb^{3}c^{9}
Multiply 36 and 8 to get 288.
288a^{2}b^{7}cc^{9}
To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.
288a^{2}b^{7}c^{10}
To multiply powers of the same base, add their exponents. Add 1 and 9 to get 10.