Question

(-2a^3b^2)^6 * (-ab/4)^3

Answer 1

Ответ:смотри решение на фото

Answer 2

To simplify the expression (-2a^3b^2)^6 * (-ab/4)^3, you can apply the properties of exponents and multiplication.

First, let's simplify each term separately:

1. Simplify (-2a^3b^2)^6: (-2a^3b^2)^6 = (-2)^6 * (a^3)^6 * (b^2)^6 = 64 * a^18 * b^12

2. Simplify (-ab/4)^3: (-ab/4)^3 = (-a/4)^3 * (b/4)^3 = (-a^3/64) * (b^3/64) = (-a^3 * b^3) / 64^2 = (-a^3 * b^3) / 4096

Now, multiply the two simplified terms together:

(64 * a^18 * b^12) * (-a^3 * b^3 / 4096)

To multiply these terms, you can multiply the numerical coefficients and add the exponents with the same base (a and b):

(64 * -a^3 * a^18 * b^3 * b^12) / 4096

Now, combine like terms:

= (64 * -a^(3+18) * b^(3+12)) / 4096

= (-64a^21b^15) / 4096

Now, you can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 64:

= (-a^21b^15) / 64

So, the simplified expression is (-a^21b^15) / 64.