Final answer:
To write the expression (36x⁴)¹/² in radical notation, convert the exponent to a fractional power. Simplify the expression by breaking down 36 and x⁴ into prime factors. Then, apply the property of radicals to simplify further and get the final answer of 6x².
Step-by-step explanation:
To write the expression (36x⁴)¹/² in radical notation, we can convert the exponent to a fractional power. The numerator of the fraction represents the power and the denominator represents the root. In this case, the numerator is 1, and the denominator is 2. So, (36x⁴)¹/² can be written as √(36x⁴).
To simplify this expression, we can break down 36 and x⁴ into their prime factors. 36 can be written as 2² × 3², and x⁴ can be written as (x²)². So, the expression becomes √(2² × 3² × (x²)²).
Using the property of radicals that √(ab) = √a × √b, we can simplify the expression further. √2² = 2, √3² = 3, and √(x²)² = x². Therefore, the final simplified expression is 2 × 3 × x², which can be written as 6x².