Given x 0 and y 0, select the expression that is equivalent to root(3)(216x^(10)y^(6)) 6x^((10)/(3))y^(2) 72x^((10)/(3))y^(2) 72x^(30)y^(18) 6x^(30)y^(18)

Question

Given  x > 0 and  y > 0, select the expression that is equivalent to  root(3)(216x^(10)y^(6))  6x^((10)/(3))y^(2)  72x^((10)/(3))y^(2)  72x^(30)y^(18)  6x^(30)y^(18)

Bytelearn · Accepted Answer

Identify Cube Root: Identify the cube root of the given expression. The cube root of a product is the product of the cube roots of each factor. So, we have root(3)(216x^(10)y^(6)) = root(3)(216) * root(3)(x^(10)) * root(3)(y^(6)).Simplify 216: Simplify the cube root of 216. 216 is a perfect cube because 216 = 6^3. Therefore, root(3)(216) = 6.Simplify x^(10): Simplify the cube root of x^(10). We can express x^(10) as x^(9) * x to make it easier to take the cube root. The cube root of x^(9) is x^(9/3) = x^3. The cube root of x is x^(1/3). Therefore, root(3)(x^(10)) = x^3 * x^(1/3) = x^(3 + 1/3) = x^(10/3).Simplify y^(6): Simplify the cube root of y^(6). Since y^(6) is a perfect cube (y^(6) = (y^2)^3), the cube root of y^(6) is y^(6/3) = y^2.Combine Simplified Roots: Combine the simplified cube roots. We have 6 * x^(10/3) * y^2. This is the expression equivalent to the original cube root.

Given x>0 and y>0 , select the expression that is equivalent to $\newline$ $\sqrt[3]{216 x^{10} y^{6}}$ $\newline$ $6 x^{\frac{10}{3}} y^{2}$ $\newline$ $72 x^{\frac{10}{3}} y^{2}$ $\newline$ $72 x^{30} y^{18}$ $\newline$ $6 x^{30} y^{18}$

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