Select the expression that is equivalent to (7x)^(-(1)/(3)) (1)/(sqrt((7x)^(3))) (1)/(root(3)(7x)) sqrt((7x)^(3)) root(3)(7x)

Understand Rule for Negative Exponents: Understand the exponent rule for negative exponents. A negative exponent indicates that the base should be taken as the reciprocal. So, (7x)^(-(1)/(3)) means we take the reciprocal of (7x) raised to the positive 1/3 power.Apply Negative Exponent Rule: Apply the negative exponent rule. Taking the reciprocal of (7x) to the positive 1/3 power, we get (1)/(7x)^(1/3).Recognize Meaning of 1/3 Exponent: Recognize the meaning of the 1/3 exponent. The exponent 1/3 corresponds to the cube root. Therefore, (7x)^(1/3) is the cube root of 7x.Combine Reciprocal and Cube Root: Combine the reciprocal and cube root. The expression (1)/(7x)^(1/3) is equivalent to taking the cube root of 7x and then taking the reciprocal of that result. This gives us the expression (1)/(root(3)(7x)).

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Select the expression that is equivalent to
(7x)^(-(1)/(3))

(1)/(sqrt((7x)^(3)))

(1)/(root(3)(7x))

sqrt((7x)^(3))

root(3)(7x)

Select the expression that is equivalent to $(7 x)^{-\frac{1}{3}}$ $\newline$ $\frac{1}{\sqrt{(7 x)^{3}}}$ $\newline$ $\frac{1}{\sqrt[3]{7 x}}$ $\newline$ $\sqrt{(7 x)^{3}}$ $\newline$ $\sqrt[3]{7 x}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the expression that is equivalent to

(7 x)^{-\frac{1}{3}}

\newline

\frac{1}{\sqrt{(7 x)^{3}}}

\newline

\frac{1}{\sqrt[3]{7 x}}

\newline

\sqrt{(7 x)^{3}}

\newline

\sqrt[3]{7 x}

Understand Rule for Negative Exponents: Understand the exponent rule for negative exponents. A negative exponent indicates that the base should be taken as the reciprocal. So, $(7x)^{-(\frac{1}{3})}$ means we take the reciprocal of $(7x)$ raised to the positive $\frac{1}{3}$ power.
Apply Negative Exponent Rule: Apply the negative exponent rule. Taking the reciprocal of $(7x)$ to the positive $\frac{1}{3}$ power, we get $\frac{1}{(7x)^{\frac{1}{3}}}$ .
Recognize Meaning of $1/3$ Exponent: Recognize the meaning of the $1/3$ exponent. $\newline$ The exponent $1/3$ corresponds to the cube root. Therefore, $(7x)^{1/3}$ is the cube root of $7x$ .
Combine Reciprocal and Cube Root: Combine the reciprocal and cube root. $\newline$ The expression $(1)/(7x)^{(1/3)}$ is equivalent to taking the cube root of $7x$ and then taking the reciprocal of that result. This gives us the expression $(1)/\sqrt[3]{7x}$ .