Answer:
n = 5
Step-by-step explanation:
Using the rules of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex] ,
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]
Given
[tex](3^{n}.3^{2} ) ^{4}[/tex] = [tex]3^{28}[/tex] , then
[tex](3^{(n+2)}) ^{4}[/tex] = [tex]3^{28}[/tex]
[tex]3^{4(n+2)}[/tex] = [tex]3^{28}[/tex]
Since the bases on both sides are equal, both 3 then equate the exponents
4(n + 2) = 28 ← divide both sides by 4
n + 2 = 7 ( subtract 2 from both sides )
n = 5
