Question

simplify:

1. 1296^.18* 1296^.07/ 3^.25* 9^.075* 27^.2

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \frac{{1296}^{.18}\times {1296}^{.07}}{3^{.25}\times 9^{.075}\times {27}^{.2}} \\ =\frac{{1296}^{.18+.07}}{3^{.25}\times {\left(3^2\right)}^{.075}\times {\left(3^3\right)}^{.2}} \\ =\frac{{1296}^{.25}}{3^{.25}\times 3^{.15}\times 3^{.6}} \\ =\frac{{\left(6\times 6\times 6\times 6\right)}^{.25}}{3^{.25+.15+.6}} \\ =\frac{{\left(6^4\right)}^{.25}}{3^1} \\ =\frac{6^{4\times .25}}{3} \\ =\frac{6^1}{3} \\ =\frac{6}{3} \\ =2 \end{gathered}$$