Select the expression that is equivalent to 6x^((4)/(3)) root(4)(6x^(3)) 6root(4)(x^(3)) root(3)(6x^(4)) 6root(3)(x^(4))

Understand given expression: Understand the given expression. The given expression is 6x^((4)/(3)), which means we are looking for an equivalent expression that represents the same quantity.Analyze the options: Analyze the options. We have four options to consider: A) root(4)(6x^(3)) B) 6root(4)(x^(3)) C) root(3)(6x^(4)) D) 6root(3)(x^(4)) We need to find which one of these is equivalent to the given expression 6x^((4)/(3)).Convert to radical form: Convert the given expression to radical form. The expression 6x^((4)/(3)) can be written in radical form as 6 * (x^(4))^(1/3), which means the cube root of x to the fourth power, multiplied by 6.Match with options: Match the converted expression with the options. Looking at the options, we can see that option D) 6root(3)(x^(4)) matches our converted expression, as it represents 6 times the cube root of x to the fourth power.Verify equivalence: Verify that the other options are not equivalent. A) root(4)(6x^(3)) is not equivalent because it represents the fourth root of the product 6x^3, not the cube root of x to the fourth power. B) 6root(4)(x^(3)) is not equivalent because it represents 6 times the fourth root of x to the third power. C) root(3)(6x^(4)) is not equivalent because it represents the cube root of the product 6x^4, not 6 times the cube root of x to the fourth power.

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Select the expression that is equivalent to
6x^((4)/(3))

root(4)(6x^(3))

6root(4)(x^(3))

root(3)(6x^(4))

6root(3)(x^(4))

Select the expression that is equivalent to $6 x^{\frac{4}{3}}$ $\newline$ $\sqrt[4]{6 x^{3}}$ $\newline$ $6 \sqrt[4]{x^{3}}$ $\newline$ $\sqrt[3]{6 x^{4}}$ $\newline$ $6 \sqrt[3]{x^{4}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the expression that is equivalent to

6 x^{\frac{4}{3}}

\newline

\sqrt[4]{6 x^{3}}

\newline

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

\newline

\sqrt[3]{6 x^{4}}

\newline

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

Understand given expression: Understand the given expression. $\newline$ The given expression is $6x^{(4/3)}$ , which means we are looking for an equivalent expression that represents the same quantity.
Analyze the options: Analyze the options. $\newline$ We have four options to consider: $\newline$ A) $\sqrt[4]{6x^{3}}$ $\newline$ B) $6\sqrt[4]{x^{3}}$ $\newline$ C) $\sqrt[3]{6x^{4}}$ $\newline$ D) $6\sqrt[3]{x^{4}}$ $\newline$ We need to find which one of these is equivalent to the given expression $6x^{\frac{4}{3}}$ .
Convert to radical form: Convert the given expression to radical form. $\newline$ The expression $6x^{(4)/(3)}$ can be written in radical form as $6 \times (x^{4})^{1/3}$ , which means the cube root of $x$ to the fourth power, multiplied by $6$ .
Match with options: Match the converted expression with the options. $\newline$ Looking at the options, we can see that option D) $6\sqrt[3]{x^{4}}$ matches our converted expression, as it represents $6$ times the cube root of $x$ to the fourth power.
Verify equivalence: Verify that the other options are not equivalent. $\newline$ A) $\sqrt[4]{6x^{3}}$ is not equivalent because it represents the fourth root of the product $6x^3$ , not the cube root of $x$ to the fourth power. $\newline$ B) $6\sqrt[4]{x^{3}}$ is not equivalent because it represents $6$ times the fourth root of $x$ to the third power. $\newline$ C) $\sqrt[3]{6x^{4}}$ is not equivalent because it represents the cube root of the product $6x^4$ , not $6$ times the cube root of $x$ to the fourth power.