Final answer:
The equivalent expression for the product √6x^18x^2 when x > 0 is 6x√3, represented by Option B. We simplify the product by combining exponents and factoring out x^20 from the square root of 6 to obtain this result.
Step-by-step explanation:
The question is asking to find an equivalent expression for the product of √6x18 and x2 when x > 0. We can simplify the expression by recognizing that x18 can be represented as (x9)2, which is the square of x9. So, we have the square root of 6 multiplied by the square of x9 and then multiplied by x2:
Since we are multiplying the same base (x), we can add the exponents (according to the rule for multiplying exponents):
Therefore, the expression simplifies to √6 × x20, which is equivalent to:
The correct choice that represents this simplified expression is Option B. 6x√3, because when we factor out an x20 from √6, what remains inside the square root is 6, and the square root of 6 can be simplified to √3 × √2, which leaves us with x20 × √3 (since x20 × √2 is just x20).