Question

find the product: (4k to the 5th power)(-2k)to the 3rd power. 5th power is inside the parenthesis and the 3rd is outside the parenthesis.
Is it -32k to the 8th power or -32k to the 2nd power?

Answer 1

(4k^5)(-2k)^3
4^5 k^5 (-2)^3 k^3
1024(-8) k^8
-8196 k^8

Now, if you meant
4(k^5)(-2k)^3
Then you do indeed have
-32k^8

When you have minus signs in the coefficient, they do not affect the exponents. Multiplying powers means add exponents. To get k^2 = k^(5-3), you'd have to have

4k^5(-2k)^-3
= -4/8 k^2

Then you'd have to take a negative power of 2, as well, making it a fraction.