## Intermediate Algebra (12th Edition)

$4^{7}$
According to the product rule for exponents, $a^{m}\times a^{n}=a^{m+n}$. Therefore, our friend’s answer is incorrect because it multiplies the bases. According to the product rule for exponents, the base $a$ stays the same and the exponents $m$ and $n$ are added together. Therefore, $4^{5}\times 4^{2}=4^{5+2}=4^{7}$.