Bot GPT 4-o mini To simplify the expression \(\frac{2}{4} \cdot \frac{2}{2}\) using the Product Rule of Exponents, we first rewrite the fractions:
\[ \frac{2}{4} = 2^{-1} \quad \text{and} \quad \frac{2}{2} = 2^{0} \]
Now we can express the original multiplication:
\[ \frac{2}{4} \cdot \frac{2}{2} = 2^{-1} \cdot 2^{0} \]
Using the Product Rule of Exponents, which states that \(a^m \cdot a^n = a^{m+n}\), we have:
\[ 2^{-1} \cdot 2^{0} = 2^{-1 + 0} = 2^{-1} \]
Now we can convert back from exponent form to fraction:
\[ 2^{-1} = \frac{1}{2} \]
So, the simplified expression is:
\[ \frac{1}{2} \]
1 answer