Given x 0 and y 0, select the expression that is equivalent to root(4)(256x^(18)y^(16)) 4x^((9)/(2))y^(4) 4x^((2)/(9))y^((1)/(4)) 64x^((2)/(9))y^((1)/(4)) 64x^((9)/(2))y^(4)

Question

Given  x > 0 and  y > 0, select the expression that is equivalent to  root(4)(256x^(18)y^(16))  4x^((9)/(2))y^(4)  4x^((2)/(9))y^((1)/(4))  64x^((2)/(9))y^((1)/(4))  64x^((9)/(2))y^(4)

Bytelearn · Accepted Answer

Identify Given Expression: Identify the given expression and understand the operation to be performed. The given expression is the fourth root of 256x^(18)y^(16), which can be written as (256x^(18)y^(16))^(1/4).Simplify Constant: Simplify the constant within the fourth root. The fourth root of 256 is 4 because 4^4 = 256. So, (256x^(18)y^(16))^(1/4) becomes (4^4x^(18)y^(16))^(1/4).Apply Exponent Property: Apply the property of exponents when taking the root of a product. The fourth root of a product is the product of the fourth roots, so we can separate the terms: (4^4x^(18)y^(16))^(1/4) = 4^(4*(1/4)) * x^(18*(1/4)) * y^(16*(1/4)).Simplify Exponents: Simplify the exponents by multiplying them with the root exponent (1/4). 4^(4*(1/4)) = 4^1 = 4. x^(18*(1/4)) = x^(18/4) = x^(9/2). y^(16*(1/4)) = y^(16/4) = y^4.Combine Terms: Combine the simplified terms to get the final expression. The equivalent expression is 4x^(9/2)y^4.

Given x>0 and y>0 , select the expression that is equivalent to $\newline$ $\sqrt[4]{256 x^{18} y^{16}}$ $\newline$ $4 x^{\frac{9}{2}} y^{4}$ $\newline$ $4 x^{\frac{2}{9}} y^{\frac{1}{4}}$ $\newline$ $64 x^{\frac{2}{9}} y^{\frac{1}{4}}$ $\newline$ $64 x^{\frac{9}{2}} y^{4}$

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