Question

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

Answer 1

To simplify the expression \( 2^4 \cdot 2^2 \) using the Product Rule of Exponents, we apply the rule which states that when multiplying two exponential expressions with the same base, we add the exponents.

In this case, the base is \( 2 \), and the exponents are \( 4 \) and \( 2 \).

So we have:

\[
2^4 \cdot 2^2 = 2^{4 + 2}
\]

Now, we add the exponents:

\[
2^{4 + 2} = 2^6
\]

Therefore, the simplified expression is:

\[
2^6
\]

If needed, \( 2^6 \) can also be calculated as:

\[
2^6 = 64
\]

So, the final answer is \( 2^6 \) or \( 64 \).