(x)/(root(3)(x)) Which of the following is equivalent to the given expression for all x!=0 ? Choose 1 answer: (A) 1 (B) root(3)(x) (c) root(3)(x^(2)) (D) x^(3)

Given expression: We are given the expression (x)/(root(3)(x)) and we need to simplify it. The cube root of x is written as x^(1/3). So we can rewrite the expression as: (x)/(x^(1/3))Rewriting the expression: To simplify the expression, we use the property of exponents that states when dividing like bases, we subtract the exponents: x^(1 - 1/3) = x^(3/3 - 1/3) = x^(2/3)Simplifying the expression: Now we have simplified the expression to x^(2/3), which is the cube root of x squared. This matches one of the answer choices provided.

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(x)/(root(3)(x))
Which of the following is equivalent to the given expression for all
x!=0 ?
Choose 1 answer:
(A) 1
(B)
root(3)(x)
(c)
root(3)(x^(2))
(D)
x^(3)

$\frac{x}{\sqrt[3]{x}}$ $\newline$ Which of the following is equivalent to the given expression for all $x \neq 0$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $1$ $\newline$ (B) $\sqrt[3]{x}$ $\newline$ (C) $\sqrt[3]{x^{2}}$ $\newline$ (D) $x^{3}$

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Math Problems

Algebra 1

Transformations of absolute value functions: translations and reflections

Full solution

\frac{x}{\sqrt[3]{x}}

\newline

Which of the following is equivalent to the given expression for all

x \neq 0

\newline

Choose

1

answer:

\newline

(A)

1

\newline

(B)

\sqrt[3]{x}

\newline

(C)

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

\newline

(D)

x^{3}

Given expression: We are given the expression $(x)/(\sqrt[3]{x})$ and we need to simplify it. The cube root of $x$ is written as $x^{1/3}$ . So we can rewrite the expression as: $(x)/(x^{1/3})$
Rewriting the expression: To simplify the expression, we use the property of exponents that states when dividing like bases, we subtract the exponents: $\newline$ $x^{1 - \frac{1}{3}} = x^{\frac{3}{3} - \frac{1}{3}} = x^{\frac{2}{3}}$
Simplifying the expression: Now we have simplified the expression to $x^{\frac{2}{3}}$ , which is the cube root of $x$ squared. This matches one of the answer choices provided.