We can start by using the definition of logarithms to rewrite the equation:
log3(x^2) = -8
This means that 3 raised to the power of -8 is equal to x^2:
3^(-8) = x^2
To solve for x, we can take the square root of both sides:
sqrt(3^(-8)) = sqrt(x^2)
On the left side, we can simplify the expression using the rule that says sqrt(a^b) = a^(b/2):
3^(-8/2) = x
Simplifying the exponent, we get:
3^(-4) = x
Recall that a negative exponent means the reciprocal of the corresponding positive exponent. So:
3^(-4) = 1/3^4
Using the exponent rule that says a^b = a*a*a*...*a (b times), we get:
1/81 = x
Therefore, the correct answer is option (D) 181.