Question

729 raised to power 3 divided by 729 divided by 3 raised to power 8?

Answer 1

Dear Student,


$$\begin{gathered} assumingthegivenquestionistosolve\frac{{\left(729\right)}^3}{{\displaystyle {\left(\frac{729}{3}\right)}^8}} \\ \Rightarrow \frac{{\displaystyle {\left(9\times 9\times 9\right)}^3}}{{\displaystyle {\left(\frac{9\times 9\times 9}{3}\right)}^8}} \\ \Rightarrow \frac{{\displaystyle {\left(9^3\right)}^3}}{{\displaystyle \frac{{\left(9^3\right)}^8}{3^8}}} \\ apply{\left(x^a\right)}^b=x^{ab} \\ \Rightarrow \frac{{\displaystyle {\left(9\right)}^9}}{{\displaystyle \frac{{\left(9\right)}^{24}}{3^8}}} \\ \Rightarrow \frac{{\displaystyle {\left(9\right)}^9\times 3^8}}{{\displaystyle {\left(9\right)}^{24}}} \\ \Rightarrow \frac{{\displaystyle 3^8}}{{\displaystyle {\left(9\right)}^{24-9}}} \\ \Rightarrow \frac{{\displaystyle 3^8}}{{\displaystyle {\left(9\right)}^{15}}} \\ \Rightarrow \frac{{\displaystyle 3^8}}{{\displaystyle {\left(3^2\right)}^{15}}} \\ \Rightarrow \frac{{\displaystyle 3^8}}{{\displaystyle {\left(3\right)}^{30}}} \\ \Rightarrow \frac{1}{3^{30-8}} \\ \Rightarrow \frac{1}{3^{22}} \end{gathered}$$
Regards,