Given x 0 and y 0, select the expression that is equivalent to sqrt(-36x^(11)y^(8)) 6ix^((2)/(11))y^((1)/(4)) -6x^((2)/(11))y^((1)/(4)) 6ix^((11)/(2))y^(4) -6x^((11)/(2))y^(4)

Question

Given  x > 0 and  y > 0, select the expression that is equivalent to  sqrt(-36x^(11)y^(8))  6ix^((2)/(11))y^((1)/(4))  -6x^((2)/(11))y^((1)/(4))  6ix^((11)/(2))y^(4)  -6x^((11)/(2))y^(4)

Bytelearn · Accepted Answer

Recognize Imaginary Unit: First, we need to recognize that the square root of a negative number involves the imaginary unit i, where i^2 = -1. So, we can rewrite the square root of -36 as 6i.Find Square Root of x^(11): Next, we need to find the square root of x^(11). Since the exponent is odd, we cannot directly take the square root. However, we can express x^(11) as x^(10) * x, and then take the square root of x^(10) which is an even exponent.Find Square Root of y^(8): The square root of x^(10) is x^(10/2) = x^5. We still have the x that was not under the square root, so we need to multiply x^5 by the square root of x, which gives us x^(5 + 1/2) = x^(11/2).Combine Parts: Now, we need to find the square root of y^(8). Since the exponent is even, we can directly take the square root. The square root of y^(8) is y^(8/2) = y^4.Compare with Options: Combining all the parts together, we have 6i times x^(11/2) times y^4. This gives us the expression 6ix^((11)/(2))y^(4).We can now compare the expression we found with the options given in the problem. The correct expression that matches our result is 6ix^((11)/(2))y^(4).

Given x>0 and y>0 , select the expression that is equivalent to $\newline$ $\sqrt{-36 x^{11} y^{8}}$ $\newline$ $6 i x^{\frac{2}{11}} y^{\frac{1}{4}}$ $\newline$ $-6 x^{\frac{2}{11}} y^{\frac{1}{4}}$ $\newline$ $6 i x^{\frac{11}{2}} y^{4}$ $\newline$ $-6 x^{\frac{11}{2}} y^{4}$

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