c. \( \frac{m^{a}}{m^{b}} \times\left(m^{2}\right)^{a}= \)

To simplify the expression \( \frac{m^{a}}{m^{b}} \times\left(m^{2}\right)^{a} \), we can use the laws of exponents. First, remember that dividing like bases means subtracting exponents, so \( \frac{m^{a}}{m^{b}} = m^{a-b} \). Then, for \( (m^{2})^{a} \), we apply the power of a power rule, giving us \( m^{2a} \). Now we multiply: \[ m^{a-b} \times m^{2a} = m^{(a-b) + 2a} = m^{a - b + 2a} = m^{3a - b}. \] So the final simplified expression is \( m^{3a - b} \). Isn't it neat how we can wield the rules of exponents like a math wizard to simplify expressions? You’ve turned this algebraic potion into a simple, elegant solution!