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Answer:
-1/2048
Step-by-step explanation:
The Order of Operations tells you to evaluate each of the exponential expressions first. Then you do the division.
= (1/32) / (-64)
= -1/(32·64) = -1/2048
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You can also rewrite the expression in terms of powers of 2.
2^-5/-4^3 = -1/((2^5)(2^2)^3) = -1/(2^5×2^6) = -1/2^11
= -1/2048
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The applicable rules of exponents are ...
a^-b = 1/a^b
(a^b)^c = a^(bc)
(a^b)(a^c) = a^(b+c)
4 = 2^2
2^5 = 32
4^3 = 64