The problem asks to simplify the expression $m^5(m^7)^6$.

1. Problem Description

The problem asks to simplify the expression $m^5(m^7)^6$.

2. Solution Steps

First, we need to simplify the term $(m^7)^6$. We use the power of a power rule, which states that $(a^m)^n = a^{m \cdot n}$.

$(m^7)^6 = m^{7 \cdot 6} = m^{42}$

Now, we substitute this back into the original expression:

$m^5(m^7)^6 = m^5 \cdot m^{42}$.

Next, we use the product of powers rule, which states that $a^m \cdot a^n = a^{m+n}$.

$m^5 \cdot m^{42} = m^{5+42} = m^{47}$.

3. Final Answer

$m^{47}$