Select the expression that is equivalent to 6x^((1)/(3)) 6sqrt(x^(3)) root(3)(6x) 6root(3)(x) sqrt(6x^(3))

Question

Select the expression that is equivalent to  6x^((1)/(3))  6sqrt(x^(3))  root(3)(6x)  6root(3)(x)  sqrt(6x^(3))

Bytelearn · Accepted Answer

Understand properties of exponents: To find the equivalent expression, we need to understand the properties of exponents and roots. The expression 6x^(1/3) represents the cube root of x multiplied by 6.Rewrite as 6 * root(3)(x): 6x^(1/3) can be rewritten as 6 * root(3)(x) because x^(1/3) is the cube root of x. This matches one of the given options.Incorrect: 6sqrt(x^(3)): 6sqrt(x^(3)) is incorrect because sqrt(x^(3)) represents the square root of x cubed, not the cube root of x.Incorrect: root(3)(6x): root(3)(6x) is incorrect because it suggests the cube root of the entire product 6x, not 6 times the cube root of x.Correct: 6root(3)(x): 6root(3)(x) is correct because it represents 6 times the cube root of x, which is exactly what 6x^(1/3) means.Incorrect: sqrt(6x^(3)): sqrt(6x^(3)) is incorrect because it represents the square root of the product 6x cubed, not the cube root of x multiplied by 6.

Select the expression that is equivalent to $6 x^{\frac{1}{3}}$ $\newline$ $6 \sqrt{x^{3}}$ $\newline$ $\sqrt[3]{6 x}$ $\newline$ $6 \sqrt[3]{x}$ $\newline$ $\sqrt{6 x^{3}}$

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Select the expression that is equivalent to $6 x^{\frac{1}{3}}$ $\newline$ $6 \sqrt{x^{3}}$ $\newline$ $\sqrt[3]{6 x}$ $\newline$ $6 \sqrt[3]{x}$ $\newline$ $\sqrt{6 x^{3}}$