Given x 0 and y 0, select the expression that is equivalent to sqrt(-100x^(7)y^(15)) 10 ix^((7)/(2))y^((15)/(2)) -10x^((7)/(2))y^((15)/(2)) 10 ix^(14)y^(30) -10x^(14)y^(30)

Question

Given  x > 0 and  y > 0, select the expression that is equivalent to  sqrt(-100x^(7)y^(15))  10 ix^((7)/(2))y^((15)/(2))  -10x^((7)/(2))y^((15)/(2))  10 ix^(14)y^(30)  -10x^(14)y^(30)

Bytelearn · Accepted Answer

Rewrite using imaginary unit: We are given the expression sqrt(-100x^(7)y^(15)). The square root of a negative number involves the imaginary unit i, where i^2 = -1. Therefore, we can rewrite the expression as sqrt(-1) * sqrt(100x^(7)y^(15)).Factor out terms: The square root of -1 is the imaginary unit i, and the square root of 100 is 10. We can then factor out these terms to get 10i * sqrt(x^(7)y^(15)).Express exponents as squares: Next, we can express x^(7) as x^(7/2)^2 and y^(15) as y^(15/2)^2 to prepare them to be taken out of the square root, since sqrt(a^2) = a.Take square roots: Taking the square root of x^(7/2)^2 and y^(15/2)^2, we get x^(7/2) and y^(15/2) respectively. Therefore, the expression becomes 10i * x^(7/2) * y^(15/2).Final expression: The final expression is 10i * x^(7/2) * y^(15/2), which is equivalent to the given expression sqrt(-100x^(7)y^(15)).

Given x>0 and y>0 , select the expression that is equivalent to $\newline$ $\sqrt{-100 x^{7} y^{15}}$ $\newline$ $10 i x^{\frac{7}{2}} y^{\frac{15}{2}}$ $\newline$ $-10 x^{\frac{7}{2}} y^{\frac{15}{2}}$ $\newline$ $10 i x^{14} y^{30}$ $\newline$ $-10 x^{14} y^{30}$

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