What is a simpler form of the radical expression?
4sqrt(2401x^12y^16)
A.) 49|x^9|y^16
B.) 49x^9|y^16|
C.)7|x^3|y^4|
D.) 7x^3|y^4|
B.) 49x^9|y^16|
To find a simplified form of the radical expression 4sqrt(2401x^12y^16), we can simplify the number under the square root first.
Since 2401 = 49 * 49, we can rewrite the expression as:
4sqrt(49 * 49 * x^12 * y^16)
Taking the square root of 49 gives us:
4 * 7 * sqrt(x^12 * y^16)
Simplifying the exponents, we get:
28 * sqrt(x^9 * y^16)
Using the property of square roots, we can split the expression into separate square roots:
28 * (sqrt(x^9) * sqrt(y^16))
Simplifying each square root individually:
28 * (x^4 * y^8)
Finally, we can combine the constants and the variables to get the simplified form:
Answer: B.) 49x^9 * y^16