Question

(\frac{4(m^{4})^{3}}{5m^{5}})

Explanation:

Step1: Simplify the numerator's exponent

Using the power of a power rule \((a^m)^n = a^{mn}\), for \((m^4)^3\), we have \(m^{4\times3}=m^{12}\). So the numerator becomes \(4m^{12}\).
The expression is now \(\frac{4m^{12}}{5m^5}\).

Step2: Simplify the variable's exponent

Using the quotient rule for exponents \(\frac{a^m}{a^n}=a^{m - n}\), for \(m^{12}\) and \(m^5\), we get \(m^{12-5}=m^7\).

Answer:

\(\frac{4m^7}{5}\)