12.

(-8x) x (3x^2)

-5x^3
-24x^2
-24x^3
-5x^2

13.
(-11z)^0

z
1
-11
1

14.
14^-4

1/14^4
-56
1/14
1/14^-4

My answer:
12. -24x^3
13. -1
14. 1/14

Correct

13 .

should have been +1

To solve these problems, we can use the rules of exponents and multiplication. Let's break down each question and explain how to find the answer.

12. To multiply two expressions, we multiply the coefficients (numbers) together and the variables with the same base (letter) by adding their exponents. In this case, we have (-8x) multiplied by (3x^2). When multiplying the coefficients -8 and 3, we get -24. For the variables with the base x, we add the exponents (-1 + 2) to get x^1. Therefore, the final answer is -24x^3.

13. Any number raised to the power of zero is always equal to 1. Therefore, (-11z)^0 equals 1. So the answer is 1.

14. To write a negative exponent as a positive exponent, we can use the rule a^-n = 1/a^n. Therefore, 14^-4 becomes 1/14^4. So the answer is 1/14^4, which is equivalent to 1/14, as 14^4 equals 14*14*14*14. So the answer is 1/14.

So, in summary:
12. (-8x) x (3x^2) = -24x^3
13. (-11z)^0 = 1
14. 14^-4 = 1/14^4 = 1/14.