Find the product: (4k^5)(-2k)^3
Is it -32k^8 or -32k^2
I don't know rather to add or subtract the 5 & 3.
The correct answer is -32k^8
- When you multiply powers with the same base, you keep the base and ADD the exponents.
- For the second multiplier, note that the both the -2 and the k would be cubed, whereas in the first multiplier only the k get raised to the 5th.
so you would (4)(k^5)(-2)^3 (k^3)
= (4)(k^5)(-8)(k^3)
= -32 k^8
To find the product (4k^5)(-2k)^3, we need to understand the rules of multiplying exponents.
The general rule is: (a^m)(a^n) = a^(m+n)
In this case, we have (4k^5)(-2k)^3, so we need to apply this rule.
First, let's simplify the expression by expanding both sets of parentheses:
(4k^5)(-2k)^3 = (4k^5)(-2^3)(k^3)
= (4k^5)(-8)(k^3)
Now, we can multiply the numbers and the exponents separately:
(4)(-8) = -32
(k^5)(k^3) = k^(5+3) = k^8
Finally, putting it all together, we get:
(4k^5)(-2k)^3 = -32k^8
Therefore, the correct answer is -32k^8.