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))

Express as Exponent: First, let's express the given radical as an exponent. root(10)(x^(21)) = x^(21/10)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 1. x^(21/10) = x^(2 + 1/10) = x^(2) * x^(1/10)Convert to Radical Form: Next, we convert the fractional exponent back to radical form. x^(2) * x^(1/10) = x^(2) * root(10)(x)Final Equivalent Expression: We have successfully expressed the original expression as a product of a whole number exponent and a radical. The final equivalent expression is x^(2)root(10)(x).

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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 , the expression $\sqrt[10]{x^{21}}$ is equivalent to $\newline$ $x \sqrt[10]{x}$ $\newline$ $x^{2} \sqrt[10]{x^{2}}$ $\newline$ $x^{2} \sqrt[10]{x}$ $\newline$ $x \sqrt[10]{x^{2}}$

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Math Problems

Algebra 2

Simplify the product of two radical expressions having same variable

Full solution

Q. Given

x>0

, the expression

\sqrt[10]{x^{21}}

is equivalent to

\newline

x \sqrt[10]{x}

\newline

x^{2} \sqrt[10]{x^{2}}

\newline

x^{2} \sqrt[10]{x}

\newline

x \sqrt[10]{x^{2}}

Express as Exponent: First, let's express the given radical as an exponent. $\sqrt[10]{x^{21}} = x^{\frac{21}{10}}$
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 $1$ . $\newline$ $x^{\frac{21}{10}} = x^{2 + \frac{1}{10}} = x^{2} \cdot x^{\frac{1}{10}}$
Convert to Radical Form: Next, we convert the fractional exponent back to radical form. $x^{2} \times x^{\frac{1}{10}} = x^{2} \times \sqrt[10]{x}$
Final Equivalent Expression: We have successfully expressed the original expression as a product of a whole number exponent and a radical. $\newline$ The final equivalent expression is $x^{2}\sqrt[10]{x}$ .