match bases
remember that if [tex]x^a=x^b[/tex] where x=x, then a=b
remember some exponential properties
[tex](a^b)^c=a^{bc}[/tex]
[tex]x^{-m}=\frac{1}{x^m}[/tex]
ok, 1/81 and 9,hmm
1/81=81^-1
81=9^2
1/81=81^-1=(9^2)^-1=9^-2
so
[tex](\frac{1}{81})^a=9^{3a+10}[/tex]
[tex](9^{-2})^a=9^{3a+10}[/tex]
[tex]9^{-2a}=9^{3a+10}[/tex]
9=9 so -2a=3a+10
-2a=3a+10
minus 3a both sides
-5a=10
divide both sides by -5
a=-2
