Given x > 0 and y > 0, select the expression that is equivalent to root(3)(216 xy^(6)) 6x^(3)y^((1)/(2)) 72x^(3)y^((1)/(2)) 6x^((1)/(3))y^(2) 72x^((1)/(3))y^(2)

Find Cube Root of 216: Simplify the cube root of 216. We know that 216 is a perfect cube, as 216 = 6^3. Therefore, the cube root of 216 is 6.Separate Product of Variables: Simplify the cube root of xy^6. Since x > 0 and y > 0, we can separate the cube root of the product into the product of the cube roots: root(3)(xy^6) = root(3)(x) * root(3)(y^6).Simplify y^6: Simplify the cube root of y^6. We know that y^6 can be written as (y^2)^3, which means the cube root of y^6 is y^2.Combine Results: Combine the simplified cube roots. Now we combine the results from Step 1 and Step 3 with the cube root of x from Step 2: 6 * root(3)(x) * y^2.Write Final Expression: Write the final expression. The final expression is 6x^(1/3)y^2.

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Given
x > 0 and
y > 0, select the expression that is equivalent to

root(3)(216 xy^(6))

6x^(3)y^((1)/(2))

72x^(3)y^((1)/(2))

6x^((1)/(3))y^(2)

72x^((1)/(3))y^(2)

Given x>0 and y>0 , select the expression that is equivalent to $\newline$ $\sqrt[3]{216 x y^{6}}$ $\newline$ $6 x^{3} y^{\frac{1}{2}}$ $\newline$ $72 x^{3} y^{\frac{1}{2}}$ $\newline$ $6 x^{\frac{1}{3}} y^{2}$ $\newline$ $72 x^{\frac{1}{3}} y^{2}$

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Math Problems

Algebra 2

Multiplication with rational exponents

Full solution

Q. Given

x>0

and

y>0

, select the expression that is equivalent to

\newline

\sqrt[3]{216 x y^{6}}

\newline

6 x^{3} y^{\frac{1}{2}}

\newline

72 x^{3} y^{\frac{1}{2}}

\newline

6 x^{\frac{1}{3}} y^{2}

\newline

72 x^{\frac{1}{3}} y^{2}

Find Cube Root of $216$ : Simplify the cube root of $216$ . We know that $216$ is a perfect cube, as $216 = 6^3$ . Therefore, the cube root of $216$ is $6$ .
Separate Product of Variables: Simplify the cube root of $xy^6$ . Since x > 0 and y > 0, we can separate the cube root of the product into the product of the cube roots: $\sqrt[3]{xy^6} = \sqrt[3]{x} \cdot \sqrt[3]{y^6}$ .
Simplify $y^6$ : Simplify the cube root of $y^6$ . We know that $y^6$ can be written as $(y^2)^3$ , which means the cube root of $y^6$ is $y^2$ .
Combine Results: Combine the simplified cube roots. $\newline$ Now we combine the results from Step $1$ and Step $3$ with the cube root of $x$ from Step $2$ : $6 \cdot \sqrt[3]{x} \cdot y^2$ .
Write Final Expression: Write the final expression. $\newline$ The final expression is $6x^{(1/3)}y^2$ .