Question

1. \\(\frac{m^4 cdot 2m^4}{(m^3)^{-4}}\\)

Explanation:

Step1: Simplify numerator (exponent rule: \(a^m \cdot a^n = a^{m + n}\))

\(m^4 \cdot 2m^4 = 2m^{4 + 4} = 2m^8\)

Step2: Simplify denominator (exponent rule: \((a^m)^n = a^{m \cdot n}\))

\((m^3)^{-4} = m^{3 \cdot (-4)} = m^{-12}\)

Step3: Rewrite fraction (exponent rule: \(a^{-n} = \frac{1}{a^n}\), so \(\frac{1}{m^{-12}} = m^{12}\))

\(\frac{2m^8}{m^{-12}} = 2m^8 \cdot m^{12}\)

Step4: Multiply exponents (rule: \(a^m \cdot a^n = a^{m + n}\))

\(2m^{8 + 12} = 2m^{20}\)

Answer:

\(2m^{20}\)