Select the expression that is equivalent to (1)/((5x)^((2)/(3))) root(3)((5x)^(2)) sqrt((5x)^(3)) (1)/(sqrt((5x)^(3))) (1)/(root(3)((5x)^(2)))

Question

Select the expression that is equivalent to  (1)/((5x)^((2)/(3)))  root(3)((5x)^(2))  sqrt((5x)^(3))  (1)/(sqrt((5x)^(3)))  (1)/(root(3)((5x)^(2)))

Bytelearn · Accepted Answer

Understand Given Expression: Understand the given expression. We are given the expression (1)/((5x)^((2)/(3))) and we need to find an equivalent expression among the options provided.Analyze Options: Analyze the options. The given expression is a fraction with a denominator that is a rational exponent. We need to find an option that represents the same relationship.Compare with First Option: Compare the given expression with the first option. The first option is root(3)((5x)^(2)). This represents the cube root of (5x) squared, which is not the same as the given expression because it is not in the form of a fraction.Compare with Second Option: Compare the given expression with the second option. The second option is sqrt((5x)^(3)). This represents the square root of (5x) cubed, which is not equivalent to the given expression because it does not have the same exponent and is not in the form of a fraction.Compare with Third Option: Compare the given expression with the third option. The third option is (1)/(sqrt((5x)^(3))). This represents the reciprocal of the square root of (5x) cubed, which is not equivalent to the given expression because the exponent is different (3/2 instead of 2/3).Compare with Fourth Option: Compare the given expression with the fourth option. The fourth option is (1)/(root(3)((5x)^(2))). This represents the reciprocal of the cube root of (5x) squared, which is exactly the same as the given expression (1)/((5x)^((2)/(3))).

Select the expression that is equivalent to $\frac{1}{(5 x)^{\frac{2}{3}}}$ $\newline$ $\sqrt[3]{(5 x)^{2}}$ $\newline$ $\sqrt{(5 x)^{3}}$ $\newline$ $\frac{1}{\sqrt{(5 x)^{3}}}$ $\newline$ $\frac{1}{\sqrt[3]{(5 x)^{2}}}$

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Select the expression that is equivalent to $\frac{1}{(5 x)^{\frac{2}{3}}}$ $\newline$ $\sqrt[3]{(5 x)^{2}}$ $\newline$ $\sqrt{(5 x)^{3}}$ $\newline$ $\frac{1}{\sqrt{(5 x)^{3}}}$ $\newline$ $\frac{1}{\sqrt[3]{(5 x)^{2}}}$