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

Given expression: We are given the expression root(3)(x^(4)), which is the cube root of x to the power of 4. We need to simplify this expression.Property of exponents: Using the property of exponents that says (x^(a/b)) = root(b)(x^a), we can rewrite the expression as x^(4/3).Splitting the exponent: Now, we can split the exponent 4/3 into two parts: 4/3 = 1 + 1/3. This allows us to write x^(4/3) as x^(1) * x^(1/3).Simplify x^(1): Since x^(1) is simply x, we can rewrite the expression as x * x^(1/3).Final simplification: The expression x * x^(1/3) can be further simplified to x * root(3)(x), because x^(1/3) is the cube root of x.

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

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

x

xroot(3)(x)

x^(2)

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

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Algebra 2

Find the vertex of the transformed function

Full solution

Q. Given

x>0

, the expression

\sqrt[3]{x^{4}}

is equivalent to

\newline

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

\newline

x

\newline

x \sqrt[3]{x}

\newline

x^{2}

Given expression: We are given the expression $\sqrt[3]{x^{4}}$ , which is the cube root of $x$ to the power of $4$ . We need to simplify this expression.
Property of exponents: Using the property of exponents that says $(x^{a/b}) = \sqrt[b]{x^a}$ , we can rewrite the expression as $x^{4/3}$ .
Splitting the exponent: Now, we can split the exponent $\frac{4}{3}$ into two parts: $\frac{4}{3} = 1 + \frac{1}{3}$ . This allows us to write $x^{\frac{4}{3}}$ as $x^{1} \times x^{\frac{1}{3}}$ .
Simplify $x^{1}$ : Since $x^{1}$ is simply $x$ , we can rewrite the expression as $x \times x^{\frac{1}{3}}$ .
Final simplification: The expression $x \times x^{\frac{1}{3}}$ can be further simplified to $x \times \sqrt[3]{x}$ , because $x^{\frac{1}{3}}$ is the cube root of $x$ .