Select the expression that is equivalent to (1)/((3x)^((5)/(4))) (1)/(root(5)((3x)^(4))) (1)/(root(4)((3x)^(5))) root(4)((3x)^(5)) root(5)((3x)^(4))

Understand given expression: Understand the given expression. The given expression is (1)/((3x)^((5)/(4))). This is a fraction with 1 in the numerator and a power expression in the denominator.Rewrite denominator using radical notation: Rewrite the denominator using radical notation. The expression (3x)^((5)/(4)) can be rewritten using radical notation. The denominator exponent (5)/(4) means the 4th root of (3x) raised to the 5th power.Apply radical notation: Apply the radical notation to the expression. The expression (1)/((3x)^((5)/(4))) is equivalent to (1)/(root(4)((3x)^(5))) because the denominator is the 4th root of (3x) to the 5th power.Check other options for equivalence: Check the other options for equivalence. Option (1)/(root(5)((3x)^(4))) is not equivalent because it represents the 5th root of (3x) to the 4th power. Option root(4)((3x)^(5)) is not equivalent because it lacks the division by 1. Option root(5)((3x)^(4)) is not equivalent because it represents the 5th root of (3x) to the 4th power.

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Select the expression that is equivalent to
(1)/((3x)^((5)/(4)))

(1)/(root(5)((3x)^(4)))

(1)/(root(4)((3x)^(5)))

root(4)((3x)^(5))

root(5)((3x)^(4))

Select the expression that is equivalent to $\frac{1}{(3 x)^{\frac{5}{4}}}$ $\newline$ $\frac{1}{\sqrt[5]{(3 x)^{4}}}$ $\newline$ $\frac{1}{\sqrt[4]{(3 x)^{5}}}$ $\newline$ $\sqrt[4]{(3 x)^{5}}$ $\newline$ $\sqrt[5]{(3 x)^{4}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the expression that is equivalent to

\frac{1}{(3 x)^{\frac{5}{4}}}

\newline

\frac{1}{\sqrt[5]{(3 x)^{4}}}

\newline

\frac{1}{\sqrt[4]{(3 x)^{5}}}

\newline

\sqrt[4]{(3 x)^{5}}

\newline

\sqrt[5]{(3 x)^{4}}

Understand given expression: Understand the given expression. $\newline$ The given expression is $(1)/((3x)^{(5)/(4)})$ . This is a fraction with $1$ in the numerator and a power expression in the denominator.
Rewrite denominator using radical notation: Rewrite the denominator using radical notation. $\newline$ The expression $3x)^{\frac{ $5$ }{ $4$ }}\ can be rewritten using radical notation. The denominator exponent \frac{\(5$}{$4$})\ means the \(4th root of \(3x)\ raised to the $5$ th power.
Apply radical notation: Apply the radical notation to the expression. $\newline$ The expression $(1)/((3x)^{(5)/(4)})$ is equivalent to $(1)/\sqrt[4]{(3x)^{5}}$ because the denominator is the $4$ th root of $(3x)$ to the $5$ th power.
Check other options for equivalence: Check the other options for equivalence. $\newline$ Option $\frac{1}{\sqrt[5]{(3x)^{4}}}$ is not equivalent because it represents the $5$ th root of $(3x)^{4}$ . $\newline$ Option $\sqrt[4]{(3x)^{5}}$ is not equivalent because it lacks the division by $1$ . $\newline$ Option $\sqrt[5]{(3x)^{4}}$ is not equivalent because it represents the $5$ th root of $(3x)^{4}$ .