nroot10^n+2^n+2 / 5^2n+(5^n)

Answer 1

To simplify this expression, we can rewrite it as follows:

(10^n + 2^n + 2) / (5^(2n) + 5^n)

Now, we can factor out a 2^n from the numerator:

= 2^n(5^n + 1) / (5^(2n) + 5^n)

Next, we notice that both terms in the denominator have a factor of 5^n. We can factor out 5^n from the denominator:

= 2^n(5^n + 1) / (5^n(5^n + 1))

Now, we can cancel out the common terms in the numerator and the denominator:

= 2^n / 5^n

Therefore, the simplified expression is 2^n / 5^n.