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

Understand Expression: Understand the given expression. The given expression is 5x^(-(5)/(4)), which means 5 times x raised to the power of negative five-fourths.Rewrite Negative Exponent: Rewrite the negative exponent as a reciprocal. A negative exponent means that the base (in this case, x) is on the bottom of a fraction, and the number 5 is multiplied by this fraction. 5x^(-(5)/(4)) = 5 / x^(5/4)Express as Radical: Express x^(5/4) as a radical. The exponent 5/4 means the fourth root of x raised to the fifth power. 5 / x^(5/4) = 5 / (root(4)(x^5))Compare with Options: Compare the expression with the given options. We need to find an option that matches the expression 5 / (root(4)(x^5)). The correct option should have a denominator with the fourth root of x to the fifth power.Eliminate Incorrect Options: Eliminate incorrect options. Option (1) (1)/(root(5)(5x^(4))) has a fifth root and a different exponent, so it's incorrect. Option (2) (5)/(root(5)(x^(4))) has a fifth root, not a fourth root, so it's incorrect. Option (3) (1)/(root(4)(5x^(5))) has the correct root but includes 5 inside the root, which is incorrect. Option (4) (5)/(root(4)(x^(5))) matches our expression from Step 3.

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

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

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

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

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

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

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the expression that is equivalent to

5 x^{-\frac{5}{4}}

\newline

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

\newline

\frac{5}{\sqrt[5]{x^{4}}}

\newline

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

\newline

\frac{5}{\sqrt[4]{x^{5}}}

Understand Expression: Understand the given expression. $\newline$ The given expression is $5x^{-(5)/(4)}$ , which means $5$ times $x$ raised to the power of negative five-fourths.
Rewrite Negative Exponent: Rewrite the negative exponent as a reciprocal. $\newline$ A negative exponent means that the base (in this case, $x$ ) is on the bottom of a fraction, and the number $5$ is multiplied by this fraction. $\newline$ $5x^{-(\frac{5}{4})} = \frac{5}{x^{\frac{5}{4}}}$
Express as Radical: Express $x^{\frac{5}{4}}$ as a radical. $\newline$ The exponent $\frac{5}{4}$ means the fourth root of $x$ raised to the fifth power. $\newline$ $\frac{5}{x^{\frac{5}{4}}} = \frac{5}{\sqrt[4]{x^5}}$
Compare with Options: Compare the expression with the given options. $\newline$ We need to find an option that matches the expression $\frac{5}{\sqrt[4]{x^5}}$ . The correct option should have a denominator with the fourth root of $x$ to the fifth power.
Eliminate Incorrect Options: Eliminate incorrect options. $\newline$ Option ( $1$ ) $\frac{1}{\sqrt[5]{5x^{4}}}$ has a fifth root and a different exponent, so it's incorrect. $\newline$ Option ( $2$ ) $\frac{5}{\sqrt[5]{x^{4}}}$ has a fifth root, not a fourth root, so it's incorrect. $\newline$ Option ( $3$ ) $\frac{1}{\sqrt[4]{5x^{5}}}$ has the correct root but includes $5$ inside the root, which is incorrect. $\newline$ Option ( $4$ ) $\frac{5}{\sqrt[4]{x^{5}}}$ matches our expression from Step $3$ .