Answer:
n=-4
Step-by-step explanation:
[tex]( \frac{5}{3} ) {}^{2n + 1} \times ( \frac{5}{3} ) {}^{5} = ( \frac{5}{3} ) {}^{n + 2} [/tex]
Apply Product of Power Rule
[tex]( \frac{5}{3} ) {}^{2n + 6 } = ( \frac{5}{3} ) {}^{n + 2} [/tex]
Set the exponents equal to each other
[tex]2n + 6 = n + 2[/tex]
[tex]n + 6 = 2[/tex]
[tex]n = - 4[/tex]
