To solve this equation, we can simplify the left side of the equation first.

32^n * 16^(-n) can be written as (2^5)^n * (2^4)^(-n).

Using the property of exponents, we can simplify this to 2^(5n) * 2^(-4n).

Now, using the property of exponents again, we can combine the two terms with the same base by adding their exponents.

2^(5n - 4n) = 2^n.

So, the equation becomes 2^n = 1024.

To solve for n, we can take the logarithm of both sides of the equation.

log(2^n) = log(1024).

Using the property of logarithms, we can bring down the exponent.

n * log(2) = log(1024).

Now, we can substitute the values of log(2) and log(1024) using a calculator.

n * 0.3010 = 3.0103.

Dividing both sides of the equation by 0.3010, we get:

n = 3.0103 / 0.3010.

Simplifying this, we find:

n ≈ 10.

Therefore, the value of n that satisfies the equation is approximately 10.