Expand a^(3+5): Simplifying Variable Exponent Expression

Expand the following equation:

$a^{3+5}=$

To solve this problem, we begin by rewriting the expression that incorporates exponent rules. The expression given is $a^{3+5}$. According to the rule of exponents, when you have a base raised to a power that is a sum, $a^{m+n} = a^m \times a^n$.

Let's apply this rule:

• Write the exponent as a sum: $3 + 5$.
• Apply the exponent rule: $a^{3+5}$ becomes $a^3 \times a^5$.

Thus, the expanded form of $a^{3+5}$ using the rule of exponents is $a^3 \times a^5$.

Finally, comparing with the provided options, choice 1 ( $a^3 \times a^5$) is the correct one, as it correctly uses the exponent rule.

Therefore, the solution to the problem is $a^3\times a^5$.