Given x 0 and y 0, select the expression that is equivalent to root(3)(-125x^(9)y^(6)) -5x^(3)y^(2) 5ix^(3)y^(2) 5ix^(27)y^(18) -5x^(27)y^(18)

Question

Given  x > 0 and  y > 0, select the expression that is equivalent to  root(3)(-125x^(9)y^(6))  -5x^(3)y^(2)  5ix^(3)y^(2)  5ix^(27)y^(18)  -5x^(27)y^(18)

Bytelearn · Accepted Answer

Identify cube root of product: Identify the cube root of a product. The cube root of a product is the product of the cube roots of each factor. So, root(3)(-125x^(9)y^(6)) = root(3)(-125) * root(3)(x^(9)) * root(3)(y^(6)).Calculate cube root of -125: Calculate the cube root of -125. The cube root of -125 is -5 because (-5)^3 = -125. root(3)(-125) = -5.Calculate cube root of x^(9): Calculate the cube root of x^(9). The cube root of x^(9) is x^(9/3) because when you take the cube root, you divide the exponent by 3. root(3)(x^(9)) = x^(9/3) = x^3.Calculate cube root of y^(6): Calculate the cube root of y^(6). The cube root of y^(6) is y^(6/3) because when you take the cube root, you divide the exponent by 3. root(3)(y^(6)) = y^(6/3) = y^2.Combine results to find equivalent expression: Combine the results to find the equivalent expression. Combining the results from steps 2, 3, and 4, we get: root(3)(-125x^(9)y^(6)) = -5 * x^3 * y^2.

Given x>0 and y>0 , select the expression that is equivalent to $\newline$ $\sqrt[3]{-125 x^{9} y^{6}}$ $\newline$ $-5 x^{3} y^{2}$ $\newline$ $5 i x^{3} y^{2}$ $\newline$ $5 i x^{27} y^{18}$ $\newline$ $-5 x^{27} y^{18}$

Full solution

More problems from Find derivatives of using multiple formulae

Related topics

Given x>0 and y>0 , select the expression that is equivalent to\newline−125x9y63 \sqrt[3]{-125 x^{9} y^{6}} 3−125x9y6​\newline−5x3y2 -5 x^{3} y^{2} −5x3y2\newline5ix3y2 5 i x^{3} y^{2} 5ix3y2\newline5ix27y18 5 i x^{27} y^{18} 5ix27y18\newline−5x27y18 -5 x^{27} y^{18} −5x27y18

Given x>0 and y>0 , select the expression that is equivalent to $\newline$ $\sqrt[3]{-125 x^{9} y^{6}}$ $\newline$ $-5 x^{3} y^{2}$ $\newline$ $5 i x^{3} y^{2}$ $\newline$ $5 i x^{27} y^{18}$ $\newline$ $-5 x^{27} y^{18}$