Answer:
Correct order : [tex]9^{-2},9^0\text{ and }9^3[/tex].
Step-by-step explanation:
Rule: If [tex]a^x[/tex] and [tex]a^y[/tex] are two numbers and a>1, then [tex]a^x>a^y[/tex] for all [tex]x>y[/tex].
The given numbers are
[tex]9^0,9^3\text{ and }9^{-2}[/tex]
It these numbers base are same, i.e., 9 which is great than 1.
We know that
[tex]-2<0<3[/tex]
Using the above rule we get
[tex]9^{-2}<9^0<9^3[/tex]
[tex]0.012345679<1<729[/tex]
Hence, the correct order from least to greatest is [tex]9^{-2},9^0\text{ and }9^3[/tex].
