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

Use Negative Exponent Property: We are given the expression (1)/((2x^(2)+3)^(-(3)/(5))). To simplify this expression, we can use the property of negative exponents which states that a^(-n) = 1/(a^n).Apply Negative Exponent Property: Applying the negative exponent property to our expression, we get: (1)/((2x^(2)+3)^(-(3)/(5))) = (2x^(2)+3)^(3/5)Simplify to Positive Exponent: Now we need to find the equivalent expression among the given options. We have simplified the original expression to (2x^(2)+3)^(3/5), which is a positive exponent form. We need to match this with one of the options.Find Equivalent Expression: Looking at the options, we can see that the equivalent expression in radical form would be the fifth root of (2x^(2)+3) raised to the third power, because the exponent 3/5 means the fifth root (denominator) of the quantity raised to the third power (numerator).Convert to Radical Form: The correct expression in radical form is therefore: root(5)((2x^(2)+3)^(3))Match with Given Options: Comparing this with the given options, we find that the equivalent expression is: (1)/(root(5)((2x^(2)+3)^(3)))

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

root(3)((2x^(2)+3)^(5))

(1)/(root(3)((2x^(2)+3)^(5)))

root(5)((2x^(2)+3)^(3))

(1)/(root(5)((2x^(2)+3)^(3)))

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

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the expression that is equivalent to

\frac{1}{\left(2 x^{2}+3\right)^{-\frac{3}{5}}}

\newline

\sqrt[3]{\left(2 x^{2}+3\right)^{5}}

\newline

\frac{1}{\sqrt[3]{\left(2 x^{2}+3\right)^{5}}}

\newline

\sqrt[5]{\left(2 x^{2}+3\right)^{3}}

\newline

\frac{1}{\sqrt[5]{\left(2 x^{2}+3\right)^{3}}}

Use Negative Exponent Property: We are given the expression $(1)/((2x^{2}+3)^{-(3)/(5)})$ . To simplify this expression, we can use the property of negative exponents which states that $a^{(-n)} = 1/(a^{n})$ .
Apply Negative Exponent Property: Applying the negative exponent property to our expression, we get: $\newline$ $(1)/((2x^{2}+3)^{-(3)/(5)}) = (2x^{2}+3)^{\frac{3}{5}}$
Simplify to Positive Exponent: Now we need to find the equivalent expression among the given options. We have simplified the original expression to $(2x^{2}+3)^{\frac{3}{5}}$ , which is a positive exponent form. We need to match this with one of the options.
Find Equivalent Expression: Looking at the options, we can see that the equivalent expression in radical form would be the fifth root of $(2x^{2}+3)$ raised to the third power, because the exponent $\frac{3}{5}$ means the fifth root (denominator) of the quantity raised to the third power (numerator).
Convert to Radical Form: The correct expression in radical form is therefore: $\sqrt[5]{(2x^{2}+3)^{3}}$
Match with Given Options: Comparing this with the given options, we find that the equivalent expression is: $\frac{1}{\sqrt[5]{(2x^{2}+3)^{3}}}$