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# Question pls

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

Thanks!!!!!!!!!!!!

May 1, 2022

#1
+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
+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?

BuilderBoi May 1, 2022
#2
+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
+1

Thank you!!

May 2, 2022