$3^{10}\times27^{2}=9^{2}\times3^n$ If $$ then what is n?

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$3^{10}\times27^{2}=9^{2}\times3^n$

$$ആയാൽ n എത്ര ?

A12

B15

C18

D24

Answer:

$3^{10}\times27^2=9^2\times3^n$

$\implies3^{10}\times(3^3)^2=(3^2)^2\times3^n$

$3^{10}\times3^6=3^4\times3^n$

$3^{10+6}=3^{4+n}$

$\implies16=4+n$

$n=12$

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