Answer:
- [tex]\frac{11}{3}[/tex]
Step-by-step explanation:
Using the rules of exponents
[tex]\frac{1}{a^{m} }[/tex] ⇔ [tex]a^{-m}[/tex]
[tex](a^{m}) ^{n}[/tex] = [tex]a^{mn}[/tex]
Consider the right side
[tex](\frac{1}{27}) ^{a+3}[/tex]
= [tex](\frac{1}{3^3}) ^{a+3}[/tex]
= [tex](3^{-3}) ^{a+3}[/tex]
= [tex]3^{(-3a-9)}[/tex]
Now we have
9 = [tex]3^{(-3a-9)}[/tex] , that is
3² = [tex]3^{(-3a-9)}[/tex]
Since the bases on both sides are equal, equate the exponents
- 3a - 9 = 2 ( add 9 to both sides )
- 3a = 11 ( divide both sides by - 3 )
a = - [tex]\frac{11}{3}[/tex]
