Given x 0 and y 0, select the expression that is equivalent to sqrt(-100x^(13)y^(8)) -10x^(26)y^(16) -10x^((13)/(2))y^(4) 10 ix^(26)y^(16) 10 ix^((13)/(2))y^(4)

Question

Given  x > 0 and  y > 0, select the expression that is equivalent to  sqrt(-100x^(13)y^(8))  -10x^(26)y^(16)  -10x^((13)/(2))y^(4)  10 ix^(26)y^(16)  10 ix^((13)/(2))y^(4)

Bytelearn · Accepted Answer

Identify Components: Identify the components of the expression inside the square root. The expression inside the square root is -100x^(13)y^(8). We need to find the square root of this expression.Factor Out -100: Factor out the square root of -100. The square root of -100 is the square root of 100 times the square root of -1, which is 10i, where i is the imaginary unit.Determine Square Root of x^(13): Determine the square root of x^(13). To find the square root of x^(13), we raise x to the power of (13/2), because the square root is equivalent to raising to the power of 1/2.Determine Square Root of y^(8): Determine the square root of y^(8). To find the square root of y^(8), we raise y to the power of (8/2), which simplifies to y^(4), because the square root of y^(8) is y^(8 * 1/2).Combine Results: Combine the results from steps 2, 3, and 4. Combining the square root of -100, which is 10i, with the square root of x^(13), which is x^((13/2)), and the square root of y^(8), which is y^(4), we get the expression 10i * x^((13/2)) * y^(4).Write Final Expression: Write the final expression. The equivalent expression for sqrt(-100x^(13)y^(8)) is 10i * x^((13/2)) * y^(4).

Given x>0 and y>0 , select the expression that is equivalent to $\newline$ $\sqrt{-100 x^{13} y^{8}}$ $\newline$ $-10 x^{26} y^{16}$ $\newline$ $-10 x^{\frac{13}{2}} y^{4}$ $\newline$ $10 i x^{26} y^{16}$ $\newline$ $10 i x^{\frac{13}{2}} y^{4}$

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