Question

reviewing laws of exponents
write the expression using a single exponent.
$-4^4(4^7)$
options: $-4^{11}$, $4^{11}$, $-16^{11}$, $-4^4$

Explanation:

Step1: Recall the law of exponents

We know that \(a^m\times a^n=a^{m + n}\), and also \(a^m\times b^m=(ab)^m\). Here we have \(-4^1\times4^7\) (note that \(-4^1\) is different from \((-4)^1\), the negative sign is not part of the base for the first term). Wait, actually the expression is \(-4^{1}(4^{7})\), which is \(-1\times4^{1}\times4^{7}\).

Step2: Apply the exponent addition rule

Using the rule \(a^m\times a^n=a^{m + n}\), for \(4^{1}\times4^{7}\), we add the exponents: \(1 + 7=11\), so \(4^{1}\times4^{7}=4^{11}\). Then multiply by \(- 1\), so \(-4^{1}\times4^{7}=-4^{11}\).

Answer:

\(-4^{11}\) (corresponding to the option \(-4_{11}\) or \(-4^{11}\) as per the given boxes, the box with \(-4^{11}\) or \(-4_{11}\) is the correct one)