Simplify

√(4 to the-1 power 3to the-2 power)

To simplify the given expression √(4^(-1) * 3^(-2)), we can start by rewriting the exponents as fractions with positive exponents:

√(1/(4^1) * 1/(3^2))

Next, we can simplify the expression inside the square root:

√(1/4 * 1/9)

Now, we can multiply the fractions:

√(1/36)

Since the square root (√) of a number is the same as raising it to the power of 1/2, we can rewrite the expression as:

(1/36)^(1/2)

To simplify further, we can simplify the numerator and denominator separately:

(1^(1/2))/(36^(1/2))

The square root of 1 is 1, and the square root of 36 is 6:

1/6

Therefore, the simplified form of √(4^(-1) * 3^(-2)) is 1/6.