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Given 
x > 0, the expression 
root(10)(x^(21)) is equivalent to

xroot( 10)(x)

x^(2)root(10)(x^(2))

x^(2)root( 10)(x)

xroot(10)(x^(2))

Given x>0 x>0 , the expression x2110 \sqrt[10]{x^{21}} is equivalent to\newlinexx10 x \sqrt[10]{x} \newlinex2x210 x^{2} \sqrt[10]{x^{2}} \newlinex2x10 x^{2} \sqrt[10]{x} \newlinexx210 x \sqrt[10]{x^{2}}

Full solution

Q. Given x>0 x>0 , the expression x2110 \sqrt[10]{x^{21}} is equivalent to\newlinexx10 x \sqrt[10]{x} \newlinex2x210 x^{2} \sqrt[10]{x^{2}} \newlinex2x10 x^{2} \sqrt[10]{x} \newlinexx210 x \sqrt[10]{x^{2}}
  1. Express as Exponent: First, let's express the given radical as an exponent. x2110=x2110\sqrt[10]{x^{21}} = x^{\frac{21}{10}}
  2. Split Exponent: Now, we can split the exponent into a sum of two terms, one of which is a whole number and the other is a fraction less than 11.\newlinex2110=x2+110=x2x110x^{\frac{21}{10}} = x^{2 + \frac{1}{10}} = x^{2} \cdot x^{\frac{1}{10}}
  3. Convert to Radical Form: Next, we convert the fractional exponent back to radical form. x2×x110=x2×x10x^{2} \times x^{\frac{1}{10}} = x^{2} \times \sqrt[10]{x}
  4. Final Equivalent Expression: We have successfully expressed the original expression as a product of a whole number exponent and a radical.\newlineThe final equivalent expression is x2x10x^{2}\sqrt[10]{x}.

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