Answer:
81
Step-by-step explanation:
Rearrange [tex]2x=3y+4[/tex] to make y the subject: [tex]y=\frac{1}{3} (2x-4)[/tex]
Just working with the denominator of [tex]\frac{9^x}{27^y} [/tex] to rewrite it using [tex]x[/tex]:
[tex]27^y=27^{\frac{1}{3}(2x-4)}[/tex]
[tex]=(27^{\frac{1}{3}})^{(2x-4)} [/tex]
[tex]=3^{(2x-4)} [/tex]
[tex]=3^{2x}[/tex] ÷ [tex]3^4[/tex]
[tex]=(3^2)^x[/tex] ÷ 81
[tex]=\frac{9^{x}}{81} [/tex]
Substitute this into [tex]\frac{9^x}{27^y} [/tex] and solve:
So [tex]9^x [/tex] ÷ [tex]27^y=9^x[/tex] ÷ [tex]\frac{9^{x}}{81} [/tex]
[tex]=9^x \times \frac{81}{9^x} [/tex]
[tex]=81[/tex]
