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, you add the exponents when multiplying the same base. The product rule states:

\[
a^m \cdot a^n = a^{m+n}
\]

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

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

Therefore, the simplified expression is:

\[
2^6
\]

If you want to express that in numerical form, \( 2^6 = 64 \).