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.