Question

calculați :[5^21÷(1+8^10÷4^14)^19-1]÷(4^15÷8^9) ​

Answer 1

Bună! ⭐

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$[5^{21} :(1+8^{10} :4^{14} )^{19} -1]:(4^{15} :8 ^{9} ) =$

$= \{ {{5^{21}:[1+(2^{3} )^{10} :(2^{2})^{14} ]^{19} -1 } \} }:[(2^{2} )^{15} :(2^{3})^{9} ]=$

$=[5^{21} :(1+2^{30} :2^{28} )^{19} -1]:(2^{30}:2^{27} )=$

$=[5^{21} :(1+2^{30-28} )^{19} -1]:2^{30-27} =$

$=[5^{21}:(1+2^{2} )^{19} -1]:2^{3} =$

$=(5^{21} :5^{19} -1):8=$

$=(5^{21-19} -1):8=$

$=(5^{2} -1):8=$

$=24:8=3$