<s>[INST] Solving $2^x \cdot 5^y = 0,128$ $x,y \in \mathbb Z$
$2^x \cdot 5^y = 0,128$
$x+y = ?$
My attempt: 
I know that
$$0,128 = \frac{128}{1000}$$
$$5^3 = 125$$
$$2^{-3} = \frac{1}{8}$$

EDIT: 
$2^7 = 128$
Then we need to get 
$0,128$
 [/INST] You know that $128=2^7$, and $1000=10^3=(2\cdot 5)^3=2^3\cdot 5^3$. Therefore
$$0.128=\frac{128}{1000}=\frac{2^7}{2^3\cdot 5^3}$$
Can you do the rest?
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