Find the product of 2^5⋅2^5 using the Product Rule of Exponents.

1 answer

To find the product of \( 2^5 \cdot 2^5 \) using the Product Rule of Exponents, we can use the rule that states:

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

In this case, we have:

  • \( a = 2 \)
  • \( m = 5 \)
  • \( n = 5 \)

Applying the Product Rule:

\[ 2^5 \cdot 2^5 = 2^{5+5} = 2^{10} \]

Now, we can calculate \( 2^{10} \):

\[ 2^{10} = 1024 \]

Thus, the product of \( 2^5 \cdot 2^5 \) is

\[ \boxed{1024} \]