Given x 0 and y 0, select the expression that is equivalent to root(3)(216x^(12)y^(8)) 72x^(4)y^((8)/(3)) 72x^((1)/(4))y^((3)/(8)) 6x^((1)/(4))y^((3)/(8)) 6x^(4)y^((8)/(3))

Question

Given  x > 0 and  y > 0, select the expression that is equivalent to  root(3)(216x^(12)y^(8))  72x^(4)y^((8)/(3))  72x^((1)/(4))y^((3)/(8))  6x^((1)/(4))y^((3)/(8))  6x^(4)y^((8)/(3))

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 need to find the cube root of 216, x^(12), and y^(8) separately.Simplify 216: Simplify the cube root of 216. 216 is a perfect cube because 216 = 6^3. Therefore, the cube root of 216 is 6.Simplify x^(12): Simplify the cube root of x^(12). The exponent rule for roots states that root(n)(a^m) = a^(m/n). Applying this rule, we get root(3)(x^(12)) = x^(12/3) = x^4.Simplify y^(8): Simplify the cube root of y^(8). Using the same exponent rule, we get root(3)(y^(8)) = y^(8/3).Combine Simplified Roots: Combine the simplified cube roots. We have the cube root of 216 as 6, x^(12) as x^4, and y^(8) as y^(8/3). Multiplying these together gives us 6x^4y^(8/3).Compare with Options: Compare the result with the given options. The expression 6x^4y^(8/3) matches one of the given options.

Given x>0 and y>0 , select the expression that is equivalent to $\newline$ $\sqrt[3]{216 x^{12} y^{8}}$ $\newline$ $72 x^{4} y^{\frac{8}{3}}$ $\newline$ $72 x^{\frac{1}{4}} y^{\frac{3}{8}}$ $\newline$ $6 x^{\frac{1}{4}} y^{\frac{3}{8}}$ $\newline$ $6 x^{4} y^{\frac{8}{3}}$

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