Answer:
n = 2
Step-by-step explanation:
Given equation:
[tex]\left(\dfrac35\right)^2 \times 25=3^n[/tex]
[tex]\textsf{Apply exponent rule }\left(\dfrac{a}{b}\right)^c=\dfrac{a^c}{b^c} :[/tex]
[tex]\implies \left(\dfrac{3^2}{5^2}\right) \times 25=3^n[/tex]
[tex]\textsf{Apply}\: \left(\dfrac{a}{b}\right) \times c=\dfrac{ac}{b} :[/tex]
[tex]\implies \dfrac{3^2\cdot 25}{5^2}=3^n[/tex]
[tex]\textsf{Apply}\:5^2=5 \times 5=25:[/tex]
[tex]\implies \dfrac{3^2\cdot 25}{25}=3^n[/tex]
Cancel the common factor 25:
[tex]\implies 3^2=3^n[/tex]
[tex]\textsf{If}\:a^{f(x)}=a^{g(x)},\:\textsf{then}\:f(x)=g(x) :[/tex]
[tex]\implies 2=n[/tex]
