Given x > 0, the expression root(5)(x^(13)) is equivalent to x^(2)root(5)(x^(3)) x^(3) xroot(5)(x^(4)) x^(2)

Understand Exponents and Roots: Understand the properties of exponents and roots. The fifth root of x to the power of 13 can be expressed as x^(13/5).Simplify Exponent: Simplify the exponent. Divide 13 by 5 to separate the exponent into a whole number and a fraction. 13 divided by 5 is 2 with a remainder of 3, so x^(13/5) = x^(2 + 3/5).Apply Exponent Properties: Apply the properties of exponents to split the expression. x^(2 + 3/5) can be written as x^2 * x^(3/5).Recognize Fifth Root: Recognize that x^(3/5) is the fifth root of x cubed. x^(3/5) is equivalent to root(5)(x^3).Combine Terms: Combine the terms to express the equivalent form. The expression root(5)(x^(13)) is equivalent to x^2 * root(5)(x^3).

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Given
x > 0, the expression
root(5)(x^(13)) is equivalent to

x^(2)root(5)(x^(3))

x^(3)

xroot(5)(x^(4))

x^(2)

Given x>0 , the expression $\sqrt[5]{x^{13}}$ is equivalent to $\newline$ $x^{2} \sqrt[5]{x^{3}}$ $\newline$ $x^{3}$ $\newline$ $x \sqrt[5]{x^{4}}$ $\newline$ $x^{2}$

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Algebra 2

Find the vertex of the transformed function

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Q. Given

x>0

, the expression

\sqrt[5]{x^{13}}

is equivalent to

\newline

x^{2} \sqrt[5]{x^{3}}

\newline

x^{3}

\newline

x \sqrt[5]{x^{4}}

\newline

x^{2}

Understand Exponents and Roots: Understand the properties of exponents and roots. $\newline$ The fifth root of $x$ to the power of $13$ can be expressed as $x^{(13/5)}$ .
Simplify Exponent: Simplify the exponent. $\newline$ Divide $13$ by $5$ to separate the exponent into a whole number and a fraction. $\newline$ $13$ divided by $5$ is $2$ with a remainder of $3$ , so $x^{(13/5)} = x^{(2 + 3/5)}$ .
Apply Exponent Properties: Apply the properties of exponents to split the expression. $\newline$ $x^{2 + \frac{3}{5}}$ can be written as $x^2 \cdot x^{\frac{3}{5}}$ .
Recognize Fifth Root: Recognize that $x^{\frac{3}{5}}$ is the fifth root of $x$ cubed. $\newline$ $x^{\frac{3}{5}}$ is equivalent to $\sqrt[5]{x^3}$ .
Combine Terms: Combine the terms to express the equivalent form. $\newline$ The expression $\sqrt[5]{x^{13}}$ is equivalent to $x^2 \cdot \sqrt[5]{x^3}$ .