Answer:
The simplified expression is:
[tex]\frac{3^9y}{2\times \:81}=\frac{243y}{2}[/tex]
Step-by-step explanation:
Given the expression
[tex]\frac{3^9\times \:y}{2\times 81}[/tex]
solving the expression
[tex]\frac{3^9\times \:y}{2\times 81}=\frac{3^9y}{162}[/tex]
[tex]=\frac{3^9y}{3^4\times \:2}[/tex] ∵ [tex]162=3^4\times \:2[/tex]
[tex]=\frac{3^5y}{2}[/tex] ∵ [tex]\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}[/tex]
[tex]=\frac{243y}{2}[/tex] ∵ [tex]3^5=243[/tex]
Therefore, the simplified expression is:
[tex]\frac{3^9y}{2\times \:81}=\frac{243y}{2}[/tex]
