To simplify the expression A = 27^10 + 9^5 / 9^13 + 27^2, we can break it down step by step:

First, let's simplify the terms with the same base:

27^10 + 27^2 = (3^3)^10 + (3^3)^2 = 3^30 + 3^6

Next, let's simplify the terms with the same base:

9^5 / 9^13 = (3^2)^5 / (3^2)^13 = 3^10 / 3^26 = 3^(10-26) = 3^-16

Now, we can rewrite the expression with the simplified terms:

A = 3^30 + 3^6 + 3^-16

Since 3^-16 is a negative exponent, we can rewrite it as the reciprocal with a positive exponent:

A = 3^30 + 3^6 + 1 / 3^16

Now, we can combine the terms with the same base:

A = 3^30 + 3^6 + 1 / 3^16

Finally, we have simplified the expression A = 27^10 + 9^5 / 9^13 + 27^2 to A = 3^30 + 3^6 + 1 / 3^16.