Question

45 в степени 3целых 1/2 - 135 в степени 3целых 1/3

Answer 1

45 ^ ( 3 1/2 ) - 135 ^ ( 3 1/3 )
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1) 45 ^ 7/2 = ( 9 * 5)^ 7/2 = ( 9 ^ 7/2 ) * ( 5 ^ 7/2 ) = ( 3 ^2 )^ 7/2 * ( 5 ^ 7/2 ) =
= (3 ^ 7) * (5 ^ 7/2 ) = (3^7 ) * ( 5^21/6 )
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2) 135 ^ 10/3 = ( 3 * 9 * 5 ) ^ 10/3 = (( 3 ^ 3 ) ^ 10/3) * 5 ^ 10/3 = (3 ^ 10) * (5 ^ 10/3) =
= (3^10) * ( 5^20/6) 
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3) 3^7 * 5^21/6 - 3^10 * 5 ^20/6 = (3 ^ 7 * 5 ^ 20/6) * ( 5 ^ 1/6 - 3 ^3 ) = 
= ( 2187 * ⁶√ 5^20 ) * ( ⁶√ 5 - 27 ) - Ответ