Question

simplify and write in exponential form: 12⁵*3⁵*3²/4^6*3⁶

Answer 1

$$\begin{gathered} \frac{{12}^5\times 3^5\times 3^2}{4^6\times 3^6} \\ =\frac{{\left(2\times 2\times 3\right)}^5\times 3^{5+2}}{{\left(2\times 2\right)}^6\times 3^6} \\ =\frac{{\left(2^2\times 3\right)}^5\times 3^7}{2^{12}\times 3^6} \\ =\frac{2^{10}\times 3^5\times 3^7}{2^{12}\times 3^6} \\ =\frac{2^{10-12}\times 3^{5+7}}{3^6} \\ =\frac{2^{-2}\times 3^{12}}{3^6} \\ =2^{-2}\times 3^{12-6} \\ =2^{-2}\times 3^6 \\ =\frac{3^6}{2^2} \end{gathered}$$