Assuming x and y are both positive, write the following expression in simplest radical form. 7sqrt(4x^(5)y^(5)) Answer:

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Assuming  x and  y are both positive, write the following expression in simplest radical form.  7sqrt(4x^(5)y^(5)) Answer:

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Identify Perfect Square Factors: Identify the perfect square factors within the radical. We have the expression 7sqrt(4x^(5)y^(5)). The number 4 is a perfect square, and we can also pair up the x's and y's into perfect squares. We can write x^(5) as x^(4) * x and y^(5) as y^(4) * y.Simplify Perfect Square Factors: Simplify the perfect square factors. Since 4 is a perfect square, we can take the square root of 4, which is 2. For x^(4) and y^(4), since both are perfect squares (x^(2))^2 and (y^(2))^2, we can take the square root of each, which gives us x^(2) and y^(2) respectively.Pull Out Square Roots: Pull out the square roots of the perfect squares from the radical. We can now rewrite the expression as 7 * 2 * x^(2) * y^(2) * sqrt(x) * sqrt(y), since we have taken the square root of the perfect squares and left the non-perfect squares inside the radical.Multiply Constants and Variables: Multiply the constants and the variables outside the radical. Multiplying 7 and 2 gives us 14. We also multiply x^(2) and y^(2) together. The expression now is 14x^(2)y^(2)sqrt(x)sqrt(y).Combine Square Roots: Combine the square roots inside the radical. Since both x and y are under a square root, we can combine them into a single square root. The expression now becomes 14x^(2)y^(2)sqrt(xy).

Assuming $x$ and $y$ are both positive, write the following expression in simplest radical form. $\newline$ $7 \sqrt{4 x^{5} y^{5}}$ $\newline$ Answer:

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Assuming $x$ and $y$ are both positive, write the following expression in simplest radical form. $\newline$ $7 \sqrt{4 x^{5} y^{5}}$ $\newline$ Answer: