Questions: (m^(-3) n^(4))^(-4)

Solution Steps

The expression is \(\left(m^{-3} n^{4}\right)^{-4}\). According to the power of a power rule, \((a^b)^c = a^{b \cdot c}\). Apply this rule to both \(m\) and \(n\): \[ \left(m^{-3}\right)^{-4} \cdot \left(n^{4}\right)^{-4} \]

Multiply the exponents for each term: \[ m^{-3 \cdot (-4)} \cdot n^{4 \cdot (-4)} \] \[ m^{12} \cdot n^{-16} \]

Rewrite \(n^{-16}\) as \(\frac{1}{n^{16}}\) to eliminate the negative exponent: \[ m^{12} \cdot \frac{1}{n^{16}} = \frac{m^{12}}{n^{16}} \]

Final Answer