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Question
If a, m, n are positive ingegers, then \[\left\{ \sqrt[m]{\sqrt[n]{a}} \right\}^{mn}\] is equal to
Options
amn
a
am/n
1
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Solution
Find the value of . `{msqrt nsqrta}^(mn)`
So,
`{msqrt nsqrta}^(mn)`= `{msqrt (a^(1/n)} }^(mn)`
= `{a^(1/n xx 1/m)}^(mn)`
= `{a^(1/n xx 1/m xxm xxn)}`
⇒ `{msqrt nsqrta}^(mn) = {a^(1/n xx 1/m xxm xxn)} `
⇒ `{msqrt nsqrta}^(mn) = a `
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