Select the equivalent expression. ((n^(-5))/(n))^((5)/(24)) (1)/(root(4)(n^(5))) root(5)(n^(4)) root(4)(n^(5)) (1)/(root(5)(n^(4)))

Simplify base: Simplify the base of the expression. We have the expression ((n^(-5))/(n))^((5)/(24)). To simplify the base, we need to apply the exponent rule a^m / a^n = a^(m-n). So, n^(-5) / n = n^(-5-1) = n^(-6).Apply exponent: Apply the simplified base to the exponent. Now we have (n^(-6))^((5)/(24)). According to the power of a power rule, (a^m)^n = a^(m*n), we multiply the exponents. So, (n^(-6))^((5)/(24)) = n^((-6)*(5/24)) = n^(-5/4).Rewrite with positive exponent: Rewrite the expression with a positive exponent. The expression n^(-5/4) can be rewritten with a positive exponent by taking the reciprocal of the base. So, n^(-5/4) = 1/(n^(5/4)).Convert to radical: Convert the exponent to a radical. The expression 1/(n^(5/4)) can be rewritten as a radical, where the denominator of the exponent becomes the index of the root. So, 1/(n^(5/4)) = 1/root(4)(n^5).Compare with options: Compare the result with the given options. The expression we have found, 1/root(4)(n^5), matches the second option: (1)/(root(4)(n^(5))).

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Select the equivalent expression.

((n^(-5))/(n))^((5)/(24))

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

root(5)(n^(4))

root(4)(n^(5))

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

Select the equivalent expression. $\newline$ $\left(\frac{n^{-5}}{n}\right)^{\frac{5}{24}}$ $\newline$ $\frac{1}{\sqrt[4]{n^{5}}}$ $\newline$ $\sqrt[5]{n^{4}}$ $\newline$ $\sqrt[4]{n^{5}}$ $\newline$ $\frac{1}{\sqrt[5]{n^{4}}}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Select the equivalent expression.

\newline

\left(\frac{n^{-5}}{n}\right)^{\frac{5}{24}}

\newline

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

\newline

\sqrt[5]{n^{4}}

\newline

\sqrt[4]{n^{5}}

\newline

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

Simplify base: Simplify the base of the expression. $\newline$ We have the expression $((n^{-5})/(n))^{(5)/(24)}$ . To simplify the base, we need to apply the exponent rule $a^m / a^n = a^{(m-n)}$ . $\newline$ So, $n^{-5} / n = n^{(-5-1)} = n^{-6}$ .
Apply exponent: Apply the simplified base to the exponent. $\newline$ Now we have $(n^{-6})^{(5/24)}$ . According to the power of a power rule, $(a^m)^n = a^{m*n}$ , we multiply the exponents. $\newline$ So, $(n^{-6})^{(5/24)} = n^{(-6)*(5/24)} = n^{-5/4}$ .
Rewrite with positive exponent: Rewrite the expression with a positive exponent. $\newline$ The expression $n^{(-5/4)}$ can be rewritten with a positive exponent by taking the reciprocal of the base. $\newline$ So, $n^{(-5/4)} = \frac{1}{n^{(5/4)}}$ .
Convert to radical: Convert the exponent to a radical. $\newline$ The expression $\frac{1}{n^{\frac{5}{4}}}$ can be rewritten as a radical, where the denominator of the exponent becomes the index of the root. $\newline$ So, $\frac{1}{n^{\frac{5}{4}}} = \frac{1}{\sqrt[4]{n^5}}$ .
Compare with options: Compare the result with the given options. $\newline$ The expression we have found, $1/\sqrt[4]{n^5}$ , matches the second option: $(1)/(\sqrt[4]{n^{5}})$ .