Final answer:
The expression ((4t²)/(121z⁴)¹⁄₂) simplifies to (2t) / (11z²) after taking the square root of both the numerator and the denominator.
Step-by-step explanation:
To simplify the expression given by ((4t²)/(121z⁴)¹⁄₂), we will first address the exponent ¹⁄₂, which indicates the square root. Therefore, the expression can be rewritten as:
√((4t²)/(121z⁴))
This can be split into two separate square roots:
√(4t²) / √(121z⁴)
Since the square root of a square number or variable is the base itself, this simplifies to:
(2t) / (11z²)
Hence, the simplified expression is:
(2t) / (11z²)
The absolute value symbols are not necessary in this case because squaring any real number will always yield a non-negative result, and the square root of a non-negative result will also be non-negative.