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已知:$(5x^4) \times (x^2)^3 \times (2x)^2$ 要求：我们将给定乘积表示为单项式，并验证结果在 x = 1 时成立：解：$(5x^4) \times (x^2)^3 \times (2x)^2= 5x^4 \times x^{2\times3} \times 2x \times 2x = 5x^4 \times x^6 \times 4x^2 = 5 \times 4 \times x^{4 + 6 + 2} = 20x^{12}$ 左边 $= (5x^4) \times (x^2)^3 \times (2x)^2 = 5 \times (1)^4 \times [(1)^2]^3 \times (2 \times 1)^2 = 5 \times 1 \times (1)^{2\times 3} \times (2)^2 = 5 \times 1^6 \times 2^2 = 5 \times 1 \times 4 = 20$ 右边 $= 20x^{12} = 20 (1)^{12} = 20 \times 1 = 20$ 因此，左边 = 右边
已知:$(x^2)^3 \times (2x) \times (-4x) \times 5$ 要求：我们将给定乘积表示为单项式，并验证结果在 x = 1 时成立：解：$(x^2)^3 \times (2x) \times (-4x) \times 5= x^{2 \times 3} \times 2x \times (-4x) \times 5 = x^6 \times 2x \times (-4x) \times 5 = 2 \times (-4) \times 5 \times x^{6+1 +1} = -40x^8$ 左边 $= (x^2)^3 \times (2x) \times (-4x) \times (5) = (1^2)^3 \times (2 \times 1) \times (-4 \times 1) \times 5 = 1^{2 \times 3} \times 2 \times (- 4) \times 5 = 1^6 \times 2 \times (-4) \times 5 = 1 \times 2 \times (-4) \times 5 = -40$ 右边 $= -40x^8 = -40 \times (1)^8 = -40 \times 1 = -40$ 因此，左边 = 右边
已知：$-8x^2y^6$ 和 $-20xy$ 要求：我们必须写下 $-8x^2y^6$ 和 $-20xy$ 的乘积，并验证当 x = 2.5, y = 1 时的乘积。解：$-8x^2y^6$ 和 $-20xy$ 的乘积是，$(-8x^2y^6) \times (-20xy) = -8 \times (-20) \times x^2 \times x \times y^6 \times y = 160x^{2 + 1} \times y^{6 + 1} = 160x^3y^7$ 左边 $= (-8x^2y^6) \times (-20xy) = -8 \times (2.5)^2 \times (1)^6 \times (-20 \times 2.5 \times 1) = -8 \times 6.25 \times 1 \times -20 \times 2.5 = (-50) \times (-50) = 2500$ 右边 $= 160 x^3y^7 = 160 (2.5)^3 \times (1)^7 = 160 \times 15.625 \times 1 =2500$ 因此，左边 = 右边
已知：$(3.2x^6y^3) \times (2.1x^2y^2)$ 要求：我们必须计算当 x = 1 且 y = 0.5 时，$(3.2x^6y^3) \times (2.1x^2y^2)$ 的值。解：$(3.2x^6y^3) \times (2.1x^2y^2)=3.2 \times 2.1 \times x^{6+2} \times y^{3+2} = 6.72x^8y^5 = 6.72 \times (1)^8 \times (0.5)^5 = 6.72 \times 1 \times 0.03125 = 0.21$
已知：$(5x^6) \times (-1.5x^2y^3) \times (-12xy^2)$ 要求：我们必须求当 x = 1, y = 0.5 时，$(5x^6) \times (-1.5x^2y^3) \times (-12xy^2)$ 的值。解：$(5 x^{6}) \times(-1.5 x^{2} y^{3}) \times(-12 x y^{2})=5 \times(-1.5) \times(-12)\times x^{6} \times x^{2} \times x \times y^{3} \times y^{2} =90 \times x^{6+2+1} \times y^{3+2} =90 \times x^{9} y^{5} =90\times (1)^{9} \times(0.5)^{5} =90 \times 1 \times 0.03125 =2.8125$
已知：$(2.3a^5b^2) \times (1.2a^2b^2)$ 要求：我们必须计算当 a = 1, b = 0.5 时，$(2.3a^5b^2) \times (1.2a^2b^2)$ 的值。解：$(2.3 a^{5} b^{2}) \times(1.2 a^{2} b^{2})=2.3 \times 1.2 \times a^{5} \times a^{2} \times b^{2} \times b^{2} =2.76 \times a^{5+2} \times b^{2+2} =2.76 \times a^{7} \times b^{4} =2.76\times(1)^{7} \times(0.5)^{4} =\frac{276}{100} \times 1 \times(\frac{1}{2})^{4} =\frac{276}{100} \times \frac{1}{16} =\frac{69}{400}$
已知：$(-8x^2y^6) \times (-20xy)$ 要求：我们必须计算当 x = 2.5, y = 1 时，$(-8x^2y^6) \times (-20xy)$ 的值。解：$(-8 x^{2} y^{6}) \times(-20 x y)=(-8) \times(-20) \times x^{2} \times x \times y^{6} \times y =160 \times x^{2+1} \times y^{6+1} =160 \times x^{3} \times y^{7} =160 \times(2.5)^{3} \times(1)^{7} =160 \times(\frac{5}{2})^{3} \times 1 =160 \times \frac{125}{8} =20 \times 125 =2500$
已知：$(-xy^3) \times (yx^3) \times (xy)$ 要求：我们必须将给定乘积表示为单项式，并验证结果在 x = 1, y = 2 时成立。解：$(-xy^3) \times (yx^3) \times (xy)=-x \times x^3 \times x \times y^3 \times y \times y = -x^{1 + 3 + 1} \times y^{3 + 1 + 1} = -x^5y^5$ 左边 $= (-xy^3) \times (yx^3) \times (xy) = (-1 \times 2^3) \times (2 \times (1)^3) \times (1 \times 2) = (-1 \times 8) \times (2 \times 1) \times (1 \times 2) = -8 \times 2 \times 2 = -32$ 右边 $=-x^5y^5 = -(1)^5 \times (2)^5 = -1 \times 32 = -32$ 因此，左边 = 右边
已知：\( \left(\frac{1}{8} x^{2} y^{4}\right) \times\left(\frac{1}{4} x^{4} y^{2}\right) \times(x y) \times 5 \) 要求：我们必须将给定乘积表示为单项式，并验证结果在 x = 1, y = 2 时成立。解：$(\frac{1}{8} x^{2} y^{4}) \times(\frac{1}{4} x^{4} y^{2}) \times(x y) \times 5=\frac{1}{8} \times \frac{1}{4} \times 5 \times x^{2} \times x^{4} \times x \times y^{4} \times y^{2} \times y =\frac{5}{32} x^{2+4+1} \times y^{4+2+1} =\frac{5}{32} x^{7} \times y^{7} =\frac{5}{32} x^{7} y^{7}$ 左边 $=(\frac{1}{8} x^{2} y^{4}) \times(\frac{1}{4} x^{4} y^{2}) \times(x y) \times 5 =\frac{1}{8} \times(1)^{2} \times(2)^{4} \times \frac{1}{4}(1)^{4}(2)^{2} \times 1 \times 2 \times 5 =\frac{1}{8} \times 1 \times 16 \times \frac{1}{4} \times 1 \times 4 \times 1 \times ... 阅读更多
已知：\( \left(\frac{2}{5} a^{2} b\right) \times\left(-15 b^{2} a c\right) \times\left(\frac{-1}{2}\right) c^{2} \) 要求：我们必须计算给定的表达式。解：$(\frac{2}{5} a^{2} b) \times(-15 b^{2} a c) \times(\frac{-1}{2}) c^{2}=\frac{2}{5} \times(-15) \times(\frac{-1}{2}) \times a^{2} \times a \times b \times b^{2} \times c \times c^{2} =3 \times a^{2+1} \times b^{1+2} \times c^{1+2} =3 a^{3} b^{3} c^{3}$