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Select the equivalent expression.

((u^(-1))/(u^(8)))^((5)/(6))

sqrt(u^(15))

(1)/(sqrt(u^(15)))

root(15)(u^(2))

(1)/(root(15)(u^(2)))

Select the equivalent expression. $\newline$ $\left(\frac{u^{-1}}{u^{8}}\right)^{\frac{5}{6}}$ $\newline$ $\sqrt{u^{15}}$ $\newline$ $\frac{1}{\sqrt{u^{15}}}$ $\newline$ $\sqrt[15]{u^{2}}$ $\newline$ $\frac{1}{\sqrt[15]{u^{2}}}$

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Simplify the product of two radical expressions having same variable

Full solution

Q. Select the equivalent expression.

\newline

\left(\frac{u^{-1}}{u^{8}}\right)^{\frac{5}{6}}

\newline

\sqrt{u^{15}}

\newline

\frac{1}{\sqrt{u^{15}}}

\newline

\sqrt[15]{u^{2}}

\newline

\frac{1}{\sqrt[15]{u^{2}}}

Simplify using Quotient Rule: First, let's simplify the expression inside the parentheses using the quotient rule of exponents, which states that $a^m / a^n = a^{(m-n)}$ . $\newline$ $((u^{-1})/(u^{8})) = u^{-1-8} = u^{-9}$
Apply Power Rule: Now, let's apply the power to the simplified expression using the power rule of exponents, which states that $(a^m)^n = a^{(m*n)}$ . $\newline$ $(u^{-9})^{(\frac{5}{6})} = u^{-9*(\frac{5}{6})} = u^{-\frac{45}{6}} = u^{-\frac{15}{2}}$
Convert to Radical Form: Next, we convert the negative exponent to a positive exponent by taking the reciprocal of the base, which gives us the expression in the form of a radical. $\newline$ $u^{-\frac{15}{2}} = \frac{1}{u^{\frac{15}{2}}} = \frac{1}{\sqrt{u^{15}}}$
Find Equivalent Expression: Now, we compare the simplified expression with the given options to find the equivalent one. $\newline$ The equivalent expression is $(1)/(\sqrt{u^{15}})$ .

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