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in simplest radical form.

x^(2)sqrt(x^(9))

in simplest radical form. $\newline$ $x^{2} \sqrt{x^{9}}$

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Roots of integers

Full solution

Q. in simplest radical form.

\newline

x^{2} \sqrt{x^{9}}

Understand and Identify Properties: Understand the expression and identify the properties of exponents and radicals that can be used. $\newline$ We have $x^{2} \times \sqrt{x^{9}}$ . The square root of $x^{9}$ can be expressed as $(x^{9})^{\frac{1}{2}}$ . According to the properties of exponents, when we raise a power to a power, we multiply the exponents.
Apply Exponent Rule: Apply the exponent rule to the square root of $x^{9}$ . $\newline$ $(x^{9})^{\frac{1}{2}} = x^{\frac{9}{2}}$ $\newline$ Now we have $x^{2} \cdot x^{\frac{9}{2}}$ .
Combine Exponents: Combine the exponents using the property of exponents that states when we multiply like bases, we add the exponents. $\newline$ $x^{2} \times x^{\frac{9}{2}} = x^{2 + \frac{9}{2}} = x^{\frac{4}{2} + \frac{9}{2}} = x^{\frac{13}{2}}$
Simplify to Simplest Form: Simplify the expression to its simplest radical form. $\newline$ The simplest radical form of $x^{\frac{13}{2}}$ is $x^{6} \cdot \sqrt{x}$ , because $x^{\frac{13}{2}}$ can be split into $x^{\frac{12}{2}} \cdot x^{\frac{1}{2}}$ , which simplifies to $x^{6} \cdot \sqrt{x}$ .

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