Simplify 13³ × 13⁴ × 13²: Multiplying Powers with Same Base

We need to simplify the expression $13^3 \times 13^4 \times 13^2$.

To do this, we'll use the multiplication rule for exponents, which states that when multiplying powers with the same base, we add the exponents. Mathematically, $a^m \times a^n = a^{m+n}$. Here, the common base is 13.

Let's apply this rule:

• The given expression is $13^3 \times 13^4 \times 13^2$.
• Using the rule, we add the exponents together: $3 + 4 + 2$.
• Calculate the total exponent: $3 + 4 + 2 = 9$.

Therefore, the simplified expression is $13^9$.

So, the solution to the problem is $13^9$.