Question

Use the Product Rule of Exponents to simplify the expression 2/4⋅2/2

Answer 1

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:

\[
\frac{1}{2}
\]