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Question Number 126161 by TheMexicanTacosG last updated on 17/Dec/20

f i n d “ a^{″}

^{a} \sqrt{a^{2}} = {({(4^{- \frac{1}{2}})}^{\frac{1}{2}})}^{- 2}

Answered by Olaf last updated on 18/Dec/20

\sqrt[a]{a^{2}} = {[{(4^{- \frac{1}{2}})}^{\frac{1}{2}}]}^{- 2} = {(4^{- \frac{1}{2}})}^{- 1} = 4^{\frac{1}{2}} = 2

a^{\frac{2}{a}} = 2

\frac{2}{a} \ln a = \ln 2

2 \ln a = a \ln 2

a^{2} = 2^{a}

a = 2 or 4

Answered by talminator2856791 last updated on 17/Dec/20

a^{\frac{2}{a}} = {({(4^{- \frac{1}{2}})}^{\frac{1}{2}})}^{- 2}

a^{\frac{1}{a}} \cdot a^{\frac{1}{a}} = {({(4^{- \frac{1}{2}})}^{\frac{1}{2}})}^{- 1} \cdot {({(4^{- \frac{1}{2}})}^{\frac{1}{2}})}^{- 1}

a^{\frac{1}{a}} = {({(4^{- \frac{1}{2}})}^{\frac{1}{2}})}^{- 1}

a^{\frac{1}{a}} = {({(4^{\frac{1}{2}} \cdot 4^{- 1})}^{\frac{1}{2}})}^{- 1}

a^{\frac{1}{a}} = {(4^{\frac{1}{4}} \cdot 4^{- \frac{1}{2}})}^{- 1}

a^{\frac{1}{a}} = (4^{- \frac{1}{4}} \cdot 4^{\frac{1}{2}})

a^{\frac{1}{a}} = 4^{\frac{1}{4}}

a = 4

Answered by JDamian last updated on 17/Dec/20

{({(4^{- \frac{1}{2}})}^{\frac{1}{2}})}^{- 2} = 4^{\frac{1}{2}} = 2^{\frac{2}{2}}

a^{\frac{2}{a}} = 2^{\frac{2}{2}} \to a = {\begin{cases} 2 \\ 4 \end{cases}

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