Question

simplify the following 12^-4 * 3^-4 * 4³

Answer 1

Dear Student,

$$\begin{gathered} {12}^{-4}\times 3^{-4}\times 4^3 \\ ={\left(2^2\times 3\right)}^{-4}\times 3^{-4}\times {\left(2^2\right)}^3 \\ =2^{-8}\times 3^{-4}\times 3^{-4}\times 2^6 \\ =2^{-8+6}\times 3^{-4-4} \\ ={\mathbf{2}}^{\mathbf{-}\mathbf{2}}\mathbf{\times }{\mathbf{3}}^{\mathbf{-}\mathbf{8}}\mathbf{}\mathbf{or}\mathbf{}\frac{\mathbf{1}}{{\mathbf{2}}^{\mathbf{2}}\mathbf{\times }{\mathbf{3}}^{\mathbf{8}}} \end{gathered}$$