Given x 0 and y 0, select the expression that is equivalent to sqrt(-36x^(4)y^(10)) -6x^((1)/(2))y^((1)/(5)) 6ix^(2)y^(5) -6x^(2)y^(5) 6ix^((1)/(2))y^((1)/(5))

Question

Given  x > 0 and  y > 0, select the expression that is equivalent to  sqrt(-36x^(4)y^(10))  -6x^((1)/(2))y^((1)/(5))  6ix^(2)y^(5)  -6x^(2)y^(5)  6ix^((1)/(2))y^((1)/(5))

Bytelearn · Accepted Answer

Identify Given Expression: Identify the given expression and the mathematical operation to be performed. We need to find the equivalent expression for sqrt(-36x^(4)y^(10)).Use Imaginary Unit: Recognize that the square root of a negative number involves the imaginary unit 'i', where i^2 = -1. Therefore, sqrt(-36x^(4)y^(10)) can be written as i * sqrt(36x^(4)y^(10)).Simplify Positive Terms: Simplify the square root of the positive part of the expression. Since 36, x^(4), and y^(10) are all perfect squares, we can take the square root of each term separately. sqrt(36x^(4)y^(10)) = sqrt(36) * sqrt(x^(4)) * sqrt(y^(10)).Calculate Square Roots: Calculate the square root of each term. sqrt(36) = 6, sqrt(x^(4)) = x^(4/2) = x^2, and sqrt(y^(10)) = y^(10/2) = y^5. So, sqrt(36x^(4)y^(10)) = 6 * x^2 * y^5.Combine Results: Combine the results from the previous steps to get the final expression. The equivalent expression is i * 6 * x^2 * y^5, which can be written as 6ix^2y^5.

Given x>0 and y>0 , select the expression that is equivalent to $\newline$ $\sqrt{-36 x^{4} y^{10}}$ $\newline$ $-6 x^{\frac{1}{2}} y^{\frac{1}{5}}$ $\newline$ $6 i x^{2} y^{5}$ $\newline$ $-6 x^{2} y^{5}$ $\newline$ $6 i x^{\frac{1}{2}} y^{\frac{1}{5}}$

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