Question

(−2a³b)³ : (2a³)7 = (-4a5)². (-a7b³)-4 =
(-x²y³)³. (x4y5)-² =​

Answer 1

Ответ:

Let's simplify each expression step by step:

1. **Expression 1:**

  \((-2a^3b)^3 : (2a^3)^7\)

  To simplify this, we can use the properties of exponents. When dividing with the same base and different exponents, you subtract the exponents. So:

  \((-2a^3b)^3 : (2a^3)^7 = (-2^3 * a^(3*3) * b^3) : (2^7 * a^(3*7))\)

  Now, use the properties of division. When dividing with the same base, subtract the exponents:

  \(= -2^3 * a^(3*3) * b^3 - 2^7 * a^(3*7)\)

  Calculate the values:

  \(= -8a^9b^3 / 128a^21\)

  Reduce the fractions by canceling common factors (in this case, 8):

  \(= -a^9b^3 / 16a^21\)

2. **Expression 2:**

  \((-4a^5)^2 * (-a^7b^3)^(-4)\)

  To simplify this, let's calculate each part separately.

  a. \((-4a^5)^2 = 16a^10\) (Squaring both the coefficient and the exponent)

  b. \((-a^7b^3)^(-4) = 1 / (-a^7b^3)^4 = 1 / (a^(7*4) * b^(3*4)) = 1 / (a^28b^12)

  Now, multiply these two results together:

  \(16a^10 * (1 / (a^28b^12)) = 16a^(10-28)b^(0-12) = 16a^(-18)b^(-12)\)

3. **Expression 3:**

  \((-x^2y^3)^3 * (x^4y^5)^(-2)\)

  Let's calculate each part separately.

  a. \((-x^2y^3)^3 = (-x^6y^9)\) (Cubing both the coefficients and exponents)

  b. \((x^4y^5)^(-2) = 1 / (x^(4*2)y^(5*2)) = 1 / (x^8y^10)\)

  Now, multiply these two results together:

  \((-x^6y^9) * (1 / (x^8y^10)) = (-x^6y^9) / (x^8y^10)

  To simplify this further, subtract the exponents when dividing with the same base:

  \(= -x^(6-8)y^(9-10) = -x^(-2)y^(-1)\)

So, the simplified expressions are:

1. \(-a^9b^3 / 16a^21\)

2. \(16a^(-18)b^(-12)\)

3. \(-x^(-2)y^(-1)\)