Sure! Let's solve the problem step-by-step.
We are given the expression:
[tex]\[ -4^4 \times 4^7 \][/tex]
Let's rewrite and simplify it step-by-step:
1. Identify the bases and exponents:
Here, we have two bases with exponents, [tex]\(-4^4\)[/tex] and [tex]\(4^7\)[/tex].
2. Simplify the expression:
Notice that [tex]\( -4^4 \)[/tex] can be considered as [tex]\( (-4)^4 \)[/tex], but we are interested in factoring and combining the exponents.
3. Combine the bases with the same exponent:
Since we need to manipulate the exponents, let’s express both terms with the same base:
[tex]\[ -4^4 \cdot 4^7 \][/tex]
Recognize that we can express [tex]\( -4 \)[/tex] as [tex]\( (-1)(4) \)[/tex], and simplify accordingly if needed. However, we see the common base is 4. Therefore, focus on combining the exponents since one term is actually negative.
4. Combine the exponents:
Since the base [tex]\(4\)[/tex] can be raised to combined exponents:
[tex]\[ (-1)(4)^4 \times 4^7 \Rightarrow -4^4 \times 4^7 \][/tex]
5. Combine the exponents:
When multiplying the same bases, we add the exponents:
[tex]\[
\begin{aligned}
-4^4 \times 4^7 &= -4^{4+7} &= -4^{11}
\end{aligned}
\][/tex]
Therefore, the given expression [tex]\( -4^4 \times 4^7 \)[/tex] simplifies to [tex]\( -4^{11} \)[/tex].
So, the correct answer is:
[tex]\[
-4^{11}
\][/tex]
