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pegah
they are not equivalent. 
because (-2)^4 is in the parenthesis so the - before 2 are together and both will go to the 4 power so the answer will be: (-2)^4 = 16 
but the other one is not in the parenthesis so the - will not go to the 4 power and the answer will be: -2^4 = -16 
so 16 is not equivalent to -16 :)))
i hope this is helpful 
have a nice day 
apologiabiology
no, becasue of PEMDAS
so parenthasees first
exponents next
mulitplciation next

(-2)^4=-2 times -2 times -2 times -2=positive number since even number of negative signs

-2^4=-1 times 2^2=-1 times 2 times 2 times 2 times 2=negative number since odd number of negative signs

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