(3x^2)^3*(4y^3)^2/(6xy)^3*3x 48m^5 n^6 p^4/(-8mn^3np) [5xy^2(x^2-3xy)-(-3x^2y^3)]/(2x^2y^2)

Question

(3x^2)^3*(4y^3)^2/(6xy)^3*3x 48m^5 n^6 p^4/(-8mn^3np) [5xy^2(x^2-3xy)-3x^2y^3)]/(2x^2y^2)

Answer 1

解1题
原式=(3x²)³Ã—(4y³)²Ã·(6xy)³Ã—3x
=3³Ã—(x²)³Ã—4²Ã—(y³)²Ã·(6³Ã—x³Ã—y³)×3x
=27×x^(2×3)×16×y^(3×2)÷216÷x³Ã·y³Ã—3x
=27×x^6×16×y^6÷216÷x³Ã·y³Ã—3x
=(27×16÷216×3)×(x^6÷x³Ã—x)×(y^6÷y³)
=6×x^(6-3+1)×y^(6-3)
=6x^4y³

解2题
原式=48m^5n^6p^4÷(-8mn³np)
=48×m^5×n^6×p^4÷(-8mn^4p)
=48÷(-8)×(m^5÷m)×(n^6÷n^4)×(p^4÷p)
=-6×m^(5-1)×n^(6-4)×p^(4-1)
=-6m^4n²p³

解3题
原式=[5xy²(x²-3xy)-3x²y³]÷(2x²y²)
=(5xy²Ã—x²-5xy²Ã—3xy-3x²y³)÷(2x²y²)
=(5x³y²-15x²y³-3x²y³)÷(2x²y²)
=(5x³y²-18x²y³)÷(2x²y²)
=5x³y²Ã·(2x²y²)-18x²y³Ã·(2x²y²)
=(5÷2)×(x³Ã·x²)×(y²Ã·y²)-(18÷2)×(x²Ã·x²)×(y³Ã·y²)
=2.5×x^(3-2)×1-9×1×y^(3-2)
=2.5x-9y追问

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Answer 2

原式=(3x²)³×(4y³)²÷(6xy)³×3x
=3³×(x²)³×4²×(y³)²÷(6³×x³×y³)×3x
=27×x^(2×3)×16×y^(3×2)÷216÷x³÷y³×3x
=27×x^6×16×y^6÷216÷x³÷y³×3x
=(27×16÷216×3)×(x^6÷x³×x)×(y^6÷y³)
=6×x^(6-3+1)×y^(6-3)
=6x^4y³

原式=48m^5n^6p^4÷(-8mn³np)
=48×m^5×n^6×p^4÷(-8mn^4p)
=48÷(-8)×(m^5÷m)×(n^6÷n^4)×(p^4÷p)
=-6×m^(5-1)×n^(6-4)×p^(4-1)
=-6m^4n²p³

原式=[5xy²(x²-3xy)-3x²y³]÷(2x²y²)
=(5xy²×x²-5xy²×3xy-3x²y³)÷(2x²y²)
=(5x³y²-15x²y³-3x²y³)÷(2x²y²)
=(5x³y²-18x²y³)÷(2x²y²)
=5x³y²÷(2x²y²)-18x²y³÷(2x²y²)
=(5÷2)×(x³÷x²)×(y²÷y²)-(18÷2)×(x²÷x²)×(y³÷y²)
=2.5×x^(3-2)×1-9×1×y^(3-2)
=2.5x-9y

Answer 3

解1题
原式=(3x²)³×(4y³)²÷(6xy)³×3x
=3³×(x²)³×4²×(y³)²÷(6³×x³×y³)×3x
=27×x^(2×3)×16×y^(3×2)÷216÷x³÷y³×3x
=27×x^6×16×y^6÷216÷x³÷y³×3x
=(27×16÷216×3)×(x^6÷x³×x)×(y^6÷y³)
=6×x^(6-3+1)×y^(6-3)
=6x^4y³
解2题
原式=48m^5n^6p^4÷(-8mn³np)
=48×m^5×n^6×p^4÷(-8mn^4p)
=48÷(-8)×(m^5÷m)×(n^6÷n^4)×(p^4÷p)
=-6×m^(5-1)×n^(6-4)×p^(4-1)
=-6m^4n²p³
解3题
原式=[5xy²(x²-3xy)-3x²y³]÷(2x²y²)
=(5xy²×x²-5xy²×3xy-3x²y³)÷(2x²y²)
=(5x³y²-15x²y³-3x²y³)÷(2x²y²)
=(5x³y²-18x²y³)÷(2x²y²)
=5x³y²÷(2x²y²)-18x²y³÷(2x²y²)
=(5÷2)×(x³÷x²)×(y²÷y²)-(18÷2)×(x²÷x²)×(y³÷y²)
=2.5×x^(3-2)×1-9×1×y^(3-2)
=2.5x-9y