Simplify: 4^(2y) × 4^(-5) × 4^(-y) × 4^6 Using Laws of Exponents

The product rule says $a^m \cdot a^n = a^{m+n}$. Think of it as: $4^2 \cdot 4^3 = (4 \cdot 4) \cdot (4 \cdot 4 \cdot 4) = 4^5$, which is 2 + 3 = 5!

Treat negative exponents just like negative numbers when adding! So $2y + (-5) + (-y) + 6$ becomes 2y - 5 - y + 6, which simplifies to y + 1.

These are like terms! Just like in algebra: 2y - y = 1y = y. Don't forget that y without a coefficient means 1y.

No! The product rule only works when the bases are exactly the same. For different bases, you'd need to convert them to the same base first (like $8 = 2^3$).

Double-check by counting! This problem has 4 terms to multiply, so your exponent should have 4 parts: 2y, -5, -y, and +6. Missing any term gives the wrong answer.