Given x > 0, the expression root(4)(x^(11)) is equivalent to x^(2)root(4)(x^(3)) x^(2) x^(3) x^(2)root(4)(x^(2))

Question Prompt: The question_prompt: What is the expression root(4)(x^(11)) equivalent to given x > 0?Simplify Expression: To simplify root(4)(x^(11)), we can express x^(11) as x^(8) * x^(3) because 8 + 3 = 11.Split Exponents: Now, we can take the fourth root of x^(8) * x^(3) separately. The fourth root of x^(8) is x^(8/4) = x^(2) because the exponent 8 is divisible by 4.Calculate Fourth Root: The fourth root of x^(3) remains as it is because the exponent 3 is not divisible by 4. So, we have x^(2) * root(4)(x^(3)).Final Expression: Therefore, the expression root(4)(x^(11)) is equivalent to x^(2) * root(4)(x^(3)), which matches one of the given options.

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Calculus

Find indefinite integrals using the substitution

Full solution

Q. Given

x>0

, the expression

\sqrt[4]{x^{11}}

is equivalent to

\newline

x^{2} \sqrt[4]{x^{3}}

\newline

x^{2}

\newline

x^{3}

\newline

x^{2} \sqrt[4]{x^{2}}

Question Prompt: The question_prompt: What is the expression $\sqrt[4]{x^{11}}$ equivalent to given x > 0?
Simplify Expression: To simplify $\sqrt[4]{x^{11}}$ , we can express $x^{11}$ as $x^{8} \times x^{3}$ because $8 + 3 = 11$ .
Split Exponents: Now, we can take the fourth root of $x^{8} \times x^{3}$ separately. The fourth root of $x^{8}$ is $x^{\frac{8}{4}} = x^{2}$ because the exponent $8$ is divisible by $4$ .
Calculate Fourth Root: The fourth root of $x^{3}$ remains as it is because the exponent $3$ is not divisible by $4$ . So, we have $x^{2} \cdot \sqrt[4]{x^{3}}$ .
Final Expression: Therefore, the expression $\sqrt[4]{x^{11}}$ is equivalent to $x^{2} \cdot \sqrt[4]{x^{3}}$ , which matches one of the given options.