Final answer:
After simplifying the expression 2√25y^8 · 4√6y^3 with the assumption that y > 0, we find that none of the provided options matches the correctly simplified expression, which is 40y^(11/2). The correct option answer is not listed in the options.
Step-by-step explanation:
The student asked which expression is equivalent to 2√25y^8 · 4√6y^3, assuming y>0. To solve this mathematical problem completely, we need to simplify the expression.
Firstly, we can simplify the square root of 25 as 5, and then take the fourth root of the product as instructed by the hint. Therefore, we have:
2√25y^8 · 4√6y^3 = 2*5y^4 · 4√6y^3 (because √y^8=y^4)
Now simplifying further, we get:
10y^4 · 4√6y^3
Since √y^3=y^(3/2), we can rewrite the expression as:
10y^4 · 4y^(3/2)
Upon multiplying, we combine the coefficients and add the exponents:
40y^(4+(3/2)) = 40y^(8/2+3/2) = 40y^(11/2)
To find a simplified form with an integer exponent, we look for an expression with a product of two powers of y that gives us y^(11/2). Since we do not have such a power of y given in the options, none of the provided answers is equivalent to the expression 2√25y^8 · 4√6y^3.
Thus, the correct option is not listed among the options given.