Final answer:
The expression [(-4) * (-5)] * (-4) + (-5) misleads the answer choices as it contains an addition, whereas the choices suggest multiplication only. The term (-4) is squared to (-4)^2, and assuming there's a typo turning the plus into multiplication, the term (-5) is also squared giving us the product of powers 4^2 * (-5)^2.
Step-by-step explanation:
To write the expression [(-4) * (-5)] * (-4) + (-5) as a product of powers, we need to factor out the common terms and use exponentiation rules. Let's look at each part of the expression separately:
The expression [(-4) * (-5)] * (-4) can be seen as ((-4)^2 * (-5)) because the term (-4) is being multiplied by itself, which can be written as a power: (-4)^2. Likewise, the term (-5) can be left as is because it is not being multiplied by itself.
Adding the second part, which is simply (-5), the entire expression can be rewritten as:
((-4)^2 * (-5)) + (-5) which can be seen to factor out the common (-5) term:
(-5)((-4)^2 + 1)
However, as none of the answer choices present this factored form but instead represent a pure product of powers, it appears the expression may have a typo, and the plus sign in the original expression might actually be intended to be a multiplication sign.
If the expression should have been [(-4) * (-5)] * (-4) * (-5), it would be [(-4)^2 * (-5)^2], fitting answer choice A) 4^2 * (-5)^2.