Answer:
x = - 2
Step-by-step explanation:
Using the rules of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]
Evaluating the numerator
9³ × 9 = [tex]9^{(3+1)}[/tex] = [tex]9^{4}[/tex] , thus
[tex]\frac{9^{4} }{9^{6} }[/tex]
= [tex]9^{(4-6)}[/tex] = [tex]9^{-2}[/tex]
and [tex]9^{-2}[/tex] = [tex]9^{x}[/tex]
Since bases on both sides are 9, then equate exponents
x = - 2
