Final answer:
The equivalent expression to the given quotient is sqrt(7x^2).
Step-by-step explanation:
To simplify the given quotient, we can apply the properties of exponents. By simplifying the expression inside the square root, we can rewrite it as sqrt(42x^5). Similarly, the expression inside the denominator can be simplified to sqrt(6x^3). Therefore, the quotient becomes sqrt(42x^5) / sqrt(6x^3).
Next, we can simplify this expression by using the property of square roots that states sqrt(a/b) = sqrt(a) / sqrt(b).
Applying this property to our expression, we get sqrt(42x^5) / sqrt(6x^3) = sqrt(42x^5 / 6x^3). Combining the like terms inside the square root, we have sqrt(7x^2). Therefore, the equivalent expression is sqrt(7x^2).