Given x 0 and y 0, select the expression that is equivalent to root(4)(81x^(6)y^(10)) 9x^((3)/(2))y^((5)/(2)) 3x^((2)/(3))y^((2)/(5)) 3x^((3)/(2))y^((5)/(2)) 9x^((2)/(3))y^((2)/(5))

Question

Given  x > 0 and  y > 0, select the expression that is equivalent to  root(4)(81x^(6)y^(10))  9x^((3)/(2))y^((5)/(2))  3x^((2)/(3))y^((2)/(5))  3x^((3)/(2))y^((5)/(2))  9x^((2)/(3))y^((2)/(5))

Bytelearn · Accepted Answer

Identify Given Expression: Identify the given expression and the goal. We need to simplify the fourth root of 81x^(6)y^(10).Express 81 as Power: Express 81 as a power of 3. 81 is 3 to the power of 4, since 3 * 3 * 3 * 3 = 81. So, we can write 81 as 3^4.Rewrite Using Power of 3: Rewrite the given expression using the power of 3. The given expression root(4)(81x^(6)y^(10)) can be rewritten as root(4)(3^4x^(6)y^(10)).Apply Property of Roots: Apply the property of roots to powers inside the radical. The fourth root of a power can be simplified by dividing the exponent by 4. So, root(4)(3^4) becomes 3^(4/4), which simplifies to 3^1 or just 3.Simplify x and y Terms: Simplify the x and y terms inside the radical. For x^(6), we divide the exponent by 4 to get x^(6/4), which simplifies to x^(3/2). For y^(10), we divide the exponent by 4 to get y^(10/4), which simplifies to y^(5/2).Combine Simplified Terms: Combine the simplified terms. The expression becomes 3 * x^(3/2) * y^(5/2).Check Provided Options: Check if any of the provided options match the simplified expression. The expression 3 * x^(3/2) * y^(5/2) matches the third option: 3x^((3)/(2))y^((5)/(2)).

Given x>0 and y>0 , select the expression that is equivalent to $\newline$ $\sqrt[4]{81 x^{6} y^{10}}$ $\newline$ $9 x^{\frac{3}{2}} y^{\frac{5}{2}}$ $\newline$ $3 x^{\frac{2}{3}} y^{\frac{2}{5}}$ $\newline$ $3 x^{\frac{3}{2}} y^{\frac{5}{2}}$ $\newline$ $9 x^{\frac{2}{3}} y^{\frac{2}{5}}$

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