3 years ago

2^m ÷ 2^ -4 = 4^5 pls help

Mathematics

1 answer:

kvv77 [185]3 years ago

4 0

Answer:

m = 6

Step-by-step explanation:

$\frac{a^{m}}{a^{-n}}=a^{m+n}\\\\$

2^m ÷ 2^ -4 = 4^5

$\frac{2^{m}}{2^{-4}}=(2^{2})^{5}\\\\\\2^{m+4} = 2^{2*5}\\\\2^{m+4} = 2^{10}$

Compare the powers,

m + 4 = 10

m = 10 - 4

m = 6

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Begin by computing the number of all the possibilities:
It is given by the following formula: $C_8^4=\frac{8!}{4!(8-4)!}= \frac{8\times7\times6\times5}{4\times3\times2}=70$
Computing the number of favorable cases:
Exactly one pair of socks with the same color means either one magenta pair,
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Number of possibilities with one magenta pair means"a magenta pair plus two socks with different colors from three possibilities" means 3 possibilities.
Same computation for the other colors.
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