Assuming xx and yy are both positive, write the following expression in simplest radical form.y, cubed, square root of, 45, x, to the power 7 , y, to the power 5 , end square rooty 3 45x 7 y 5
Question
Assuming xx and yy are both positive, write the following expression in simplest radical form.y, cubed, square root of, 45, x, to the power 7 , y, to the power 5 , end square rooty 3 45x 7 y 5
Solution
The expression you provided is a bit unclear, but I'm assuming you're asking to simplify the cube root of (45x^7y^5). Here's how you can do it:
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Break down the numbers and variables inside the cube root into their prime factors:
∛(45x^7y^5) = ∛(3^2*5x^7y^5)
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For cube roots, we need three of the same factor to pull it out of the root. So, we can't simplify 45 (3^2*5) any further because it doesn't have three of the same factor.
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For x^7, we can pull out two x^2 (because 2*3=6 and 6<7) from the cube root and leave one x inside the root (because 7-6=1).
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For y^5, we can pull out one y (because 1*3=3 and 3<5) from the cube root and leave two y inside the root (because 5-3=2).
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Therefore, the simplified form of the expression is:
x^2y∛(45xy^2)
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