Which expressions are equivalent to (root(4)(x))^(-1) ? Choose all answers that apply: A x^(-4) B (sqrtx)^(-4) c -root(4)(x) D None of the above

Step 1: Understand the expression: Understand the expression (root(4)(x))^(-1). The expression represents the fourth root of x, raised to the power of -1. This means we are looking for the reciprocal of the fourth root of x.Step 2: Simplify the expression: Simplify the expression using the properties of exponents. The reciprocal of a number is the same as raising that number to the power of -1. Therefore, (root(4)(x))^(-1) is the same as x^(-1/4).Step 3: Compare with given choices: Compare the simplified expression with the given choices. A. x^(-4) is not equivalent because it represents x raised to the power of -4, not -1/4. B. (sqrtx)^(-4) is not equivalent because it represents the square root of x raised to the power of -4, which is x^(-2), not x^(-1/4). C. -root(4)(x) is not equivalent because it represents the negative fourth root of x, not the reciprocal of the fourth root of x. D. None of the above is the correct choice because none of the given options match x^(-1/4).

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Which expressions are equivalent to
(root(4)(x))^(-1) ?
Choose all answers that apply:
A
x^(-4)
B
(sqrtx)^(-4)
c
-root(4)(x)
D None of the above

Which expressions are equivalent to $(\sqrt[4]{x})^{-1}$ ? $\newline$ Choose all answers that apply: $\newline$ A $x^{-4}$ $\newline$ B $(\sqrt{x})^{-4}$ $\newline$ c $-\sqrt[4]{x}$ $\newline$ D None of the above

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Math Problems

Grade 7

Identify equivalent linear expressions I

Full solution

Q. Which expressions are equivalent to

(\sqrt[4]{x})^{-1}

\newline

Choose all answers that apply:

\newline

x^{-4}

\newline

(\sqrt{x})^{-4}

\newline

-\sqrt[4]{x}

\newline

D None of the above

Step $1$ : Understand the expression: Understand the expression $(\sqrt[4]{x})^{-1}$ . The expression represents the fourth root of $x$ , raised to the power of $-1$ . This means we are looking for the reciprocal of the fourth root of $x$ .
Step $2$ : Simplify the expression: Simplify the expression using the properties of exponents. $\newline$ The reciprocal of a number is the same as raising that number to the power of $-1$ . Therefore, $(\sqrt[4]{x})^{-1}$ is the same as $x^{-\frac{1}{4}}$ .
Step $3$ : Compare with given choices: Compare the simplified expression with the given choices. $\newline$ A. $x^{(-4)}$ is not equivalent because it represents $x$ raised to the power of $-4$ , not $-\frac{1}{4}$ . $\newline$ B. $(\sqrt{x})^{(-4)}$ is not equivalent because it represents the square root of $x$ raised to the power of $-4$ , which is $x^{(-2)}$ , not $x^{(-\frac{1}{4})}$ . $\newline$ C. $-\sqrt[4]{x}$ is not equivalent because it represents the negative fourth root of $x$ , not the reciprocal of the fourth root of $x$ . $\newline$ D. None of the above is the correct choice because none of the given options match $x^{(-\frac{1}{4})}$ .