Simplify the Product: 6³ × 6⁵ × 6⁶ × 6⁴ Using Laws of Exponents

The multiplication rule for exponents states that $a^m \times a^n = a^{m+n}$. Think of it this way: $6^3$ means 6 × 6 × 6, so when you multiply by $6^5$, you're adding more 6's to multiply together!

If the bases are different (like $6^3 \times 7^5$), you cannot combine them using exponent rules. The multiplication rule only works when the bases are identical.

Multiplying same bases: add exponents ($6^3 \times 6^5 = 6^{3+5}$)
Power of a power: multiply exponents ($(6^3)^5 = 6^{3 \times 5}$)

You could calculate each power separately and then multiply the results, but that would involve huge numbers! For example, $6^6 = 46,656$ alone. The exponent rules make it much simpler.

$6^{18}$ is an extremely large number - over 100 trillion! In most math problems, leaving the answer in exponential form like $6^{18}$ is preferred and more practical.