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It turns out that (0.125)^3 can be written as 2^a for some integer a. Find a.

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 May 1, 2022

Best Answer 

 #1
avatar+1366 
+2

Note that \(\large{0.125 = {1 \over 8}}\). This can be written as \(\large{1 \over 2^3}\) or \(\large{2^{-3}}\)

 

We now have \((2^{-3})^3\). We can simplify this by multiplying the exponents. 

 

Can you solve it now?

 May 1, 2022
 #1
avatar+1366 
+2
Best Answer

Note that \(\large{0.125 = {1 \over 8}}\). This can be written as \(\large{1 \over 2^3}\) or \(\large{2^{-3}}\)

 

We now have \((2^{-3})^3\). We can simplify this by multiplying the exponents. 

 

Can you solve it now?

BuilderBoi May 1, 2022
 #2
avatar+675 
0

\((\frac{1}{8})^3 = \frac{1}{512} = 2^a \ |\cdot 512 \\ 1 = 2^{a+9}\)


We can always express 1 as n2 ! Let n be 2:

 

\(2^0 = 2^{a+9}\)

 

because if nm + a = nd + k, then it applies m + a = d + k:

 

 0 = a + 9 | - 9

-9 = a

a = -9

 

That's the only possible solution.

 May 2, 2022
 #3
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+1

Thank you!!

 May 2, 2022

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