Question

А)(-10x^2y)^3•0,0001y^3x; б)-3a^3b^2c)^3•(0,2a^2bc)^2. P.S ответ и решение обизательны

Answer 1

Ответ:

$( - 10x {}^{2} y) {}^{3} \times 0.0001y {}^{3} x = - (10x {}^{2} y {}^{3} \times 0.0001y {}^{3} x = - 1000x {}^{6} y {}^{3} \times 0.0001y {}^{3} x = - 0.1x {}^{7} y {}^{6}$

$(- 3a {}^{3} b {}^{2} c) {}^{3} \times(0.2a {}^{2} bc) {}^{2} = - 3a {}^{3} b {}^{2} c \times 0.2 {}^{2} \times a {}^{4} b {}^{2} c {}^{2} = - 3a {}^{3} b {}^{2} c \times ( \frac{1}{5} ) {}^{2} \times a {}^{4} b {}^{2} c = - 3a {}^{3} b {}^{2} c \times \frac{1}{25} a {}^{4} b {}^{2} c = - \frac{3}{25} a {}^{7} b {}^{4} c {}^{3}$

Answer 2

a) (-10x^2y)^3 • 0.0001y^3x

To simplify the expression, let's break it down step by step:

1. Start by simplifying the expression within the parentheses: (-10x^2y)^3. To raise a power to a power, we multiply the exponents, so we have (-10)^3 * (x^2)^3 * y^3. - (-10)^3 = -1000 - (x^2)^3 = x^(2*3) = x^6 - y^3 remains the same

Therefore, (-10x^2y)^3 simplifies to -1000x^6y^3.

2. Now, multiply the simplified expression by 0.0001y^3x: - -1000x^6y^3 * 0.0001y^3x = -1000 * 0.0001 * x^6 * y^3 * y^3 * x - Simplifying further, we have -0.1x^6y^6x.

So, the simplified expression for (-10x^2y)^3 • 0.0001y^3x is -0.1x^6y^6x.

b) (-3a^3b^2c)^3 • (0.2a^2bc)^2

Let's simplify the expression step by step:

1. Start by simplifying the expression within the first set of parentheses: (-3a^3b^2c)^3. To raise a power to a power, we multiply the exponents, so we have (-3)^3 * (a^3)^3 * (b^2)^3 * c^3. - (-3)^3 = -27 - (a^3)^3 = a^(3*3) = a^9 - (b^2)^3 = b^(2*3) = b^6 - c^3 remains the same

Therefore, (-3a^3b^2c)^3 simplifies to -27a^9b^6c^3.

2. Now, simplify the expression within the second set of parentheses: (0.2a^2bc)^2. To raise a power to a power, we multiply the exponents, so we have (0.2)^2 * (a^2)^2 * b^2 * c^2. - (0.2)^2 = 0.04 - (a^2)^2 = a^(2*2) = a^4 - b^2 remains the same - c^2 remains the same

Therefore, (0.2a^2bc)^2 simplifies to 0.04a^4b^2c^2.

3. Finally, multiply the simplified expressions: -27a^9b^6c^3 * 0.04a^4b^2c^2. - Multiplying the coefficients: -27 * 0.04 = -1.08 - Multiplying the variables: a^9 * a^4 = a^(9+4) = a^13, b^6 * b^2 = b^(6+2) = b^8, and c^3 * c^2 = c^(3+2) = c^5.

Therefore, (-3a^3b^2c)^3 • (0.2a^2bc)^2 simplifies to -1.08a^13b^8c^5.

I hope this helps! Let me know if you have any further questions.