Select the expression that is equivalent to (1)/((7x)^((4)/(3))) (1)/(root(3)((7x)^(4))) root(3)((7x)^(4)) (1)/(root(4)((7x)^(3))) root(4)((7x)^(3))

Understand Given Expression: Understand the given expression. We are given the expression (1)/((7x)^((4)/(3))) and we need to find an equivalent expression. The exponent (4)/(3) can be interpreted as ＂the cube root of the quantity raised to the fourth power.＂Rewrite Using Radical Notation: Rewrite the given expression using radical notation. The expression (1)/((7x)^((4)/(3))) can be rewritten using the radical notation as (1)/(root(3)((7x)^(4))).Compare with Options: Compare the rewritten expression with the options. We have the expression (1)/(root(3)((7x)^(4))) from Step 2. Now we compare this with the given options: - (1)/(root(3)((7x)^(4))) is the same as our rewritten expression. - root(3)((7x)^(4)) is not equivalent because it lacks the division by 1. - (1)/(root(4)((7x)^(3))) is not equivalent because the root and the exponent do not match the original expression. - root(4)((7x)^(3)) is not equivalent for the same reason as the previous option.Select Correct Expression: Select the correct equivalent expression. The correct equivalent expression is (1)/(root(3)((7x)^(4))) because it matches the original expression when rewritten using radical notation.

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Select the expression that is equivalent to
(1)/((7x)^((4)/(3)))

(1)/(root(3)((7x)^(4)))

root(3)((7x)^(4))

(1)/(root(4)((7x)^(3)))

root(4)((7x)^(3))

Select the expression that is equivalent to $\frac{1}{(7 x)^{\frac{4}{3}}}$ $\newline$ $\frac{1}{\sqrt[3]{(7 x)^{4}}}$ $\newline$ $\sqrt[3]{(7 x)^{4}}$ $\newline$ $\frac{1}{\sqrt[4]{(7 x)^{3}}}$ $\newline$ $\sqrt[4]{(7 x)^{3}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the expression that is equivalent to

\frac{1}{(7 x)^{\frac{4}{3}}}

\newline

\frac{1}{\sqrt[3]{(7 x)^{4}}}

\newline

\sqrt[3]{(7 x)^{4}}

\newline

\frac{1}{\sqrt[4]{(7 x)^{3}}}

\newline

\sqrt[4]{(7 x)^{3}}

Understand Given Expression: Understand the given expression. $\newline$ We are given the expression $(1)/((7x)^{(4)/(3)})$ and we need to find an equivalent expression. The exponent $(4)/(3)$ can be interpreted as ＂the cube root of the quantity raised to the fourth power.＂
Rewrite Using Radical Notation: Rewrite the given expression using radical notation. $\newline$ The expression $(1)/((7x)^{(4)/(3)})$ can be rewritten using the radical notation as $(1)/\sqrt[3]{(7x)^{4}}$ .
Compare with Options: Compare the rewritten expression with the options. $\newline$ We have the expression $(1)/(\sqrt[3]{(7x)^{4}})$ from Step $2$ . Now we compare this with the given options: $\newline$ - $(1)/(\sqrt[3]{(7x)^{4}})$ is the same as our rewritten expression. $\newline$ - $\sqrt[3]{(7x)^{4}}$ is not equivalent because it lacks the division by $1$ . $\newline$ - $(1)/(\sqrt[4]{(7x)^{3}})$ is not equivalent because the root and the exponent do not match the original expression. $\newline$ - $\sqrt[4]{(7x)^{3}}$ is not equivalent for the same reason as the previous option.
Select Correct Expression: Select the correct equivalent expression. $\newline$ The correct equivalent expression is $(\frac{1}{\sqrt[3]{(7x)^{4}}})$ because it matches the original expression when rewritten using radical notation.