Use the product rule of exponents to simplify the expression 2^4 2^2

1 answer

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, \( 2^6 = 64 \).