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Given: $2^{x} \cdot 2^{y}=32$. Calculate $x+y=?$
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According to the laws of exponents, when multiplying powers with the same base, we add the exponents. Therefore, $2^{x} \cdot 2^{y}=2^{x+y}$. According to the information provided, $2^{x+y}=32 .$ In order to find the value of $\mathrm{x}+\mathrm{y}, 32$ must be expressed as a power of base 2, that is, $32=2^{5}$. It follows that $2^{x+y}=2^{5}$. When two powers are equal and have the same base, their exponents are also equal, and we can therefore deduce that $x+y=5$.
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