Simplify 4^5 × 4^5: Multiplying Powers with Same Base

To simplify the expression $4^5 \times 4^5$, we will use the rule of exponents that states when multiplying two powers with the same base, you can add the exponents. This rule can be expressed as:

• $a^m \times a^n = a^{m+n}$

In this equation, both terms $4^5$ have the same base $4$.

According to the multiplication of powers rule:

• $4^5 \times 4^5 = 4^{5+5}$

Now, simply add the exponents:

$4^{5+5} = 4^{10}$

The simplified form of $4^5 \times 4^5$ is therefore $4^{10}$.