Rewrite this formula using rational exponents.

Question

t = 2 pi sqrt 4/32

Thanks!!!

Answer 1

sqrt ( 4 / 32 ) =

sqrt [ 4 / ( 4 * 8 ) ] =

sqrt ( 1 / 8 ) =

sqrt [ 1 / ( 4 * 2 ) ] =

sqrt ( 1 ) / [ sqrt ( 4 ) * sqrt ( 2 ) ] =

1 / 2 sqrt ( 2 )

2 pi sqrt ( 4 / 32 ) =

2 pi * 1 / 2 sqrt ( 2 ) =

pi / sqrt ( 2 ) =

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Remark:

sqrt ( 2 ) = 2 ^ ( 1 / 2 )

1 / sqrt ( 2 ) = 2 ^ ( - 1 / 2 )
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pi * 2 ^ ( - 1 / 2 )

t = 2 pi sqrt ( 4 / 32 ) = pi * 2 ^ ( - 1 / 2 )