Product Rule

When you multiply two powers with the same base, you add the exponents: $x^a \times x^b = x^{a+b}$.

For example, $2^3 \times 2^4 = (2 \times 2 \times 2) \times (2 \times 2 \times 2 \times 2) = 2^7$. You're multiplying 2 by itself $3 + 4 = 7$ times total.

This rule lets you simplify expressions without expanding everything. Instead of computing $2^{50} \times 2^{30}$ as giant numbers, you just write $2^{80}$. Clean and fast.